Recent zbMATH articles in MSC 81https://zbmath.org/atom/cc/812024-09-27T17:47:02.548271ZWerkzeugPopper, Bohr and the contextuability in quantum mechanicshttps://zbmath.org/1541.010182024-09-27T17:47:02.548271Z"Poinat, Sébastien"https://zbmath.org/authors/?q=ai:poinat.sebastienSummary: During his intellectual life, Karl Popper blamed Niels Bohr for defending subjectivist theses about Quantum Mechanics and for introducing the concept of subject in physics. But Popper's accusation contradicts Bohr's texts. The goal of this article is to show that Popper did not take seriously a central point of Bohr's position: the contextuality of quantum phenomena. Quantum contextuality has strong consequences on the nature of measurement and on the constitution of the object in Quantum Mechanics. I try to show that this misunderstanding is the reason why Popper accused Bohr for being a subjectivist.Reforming Takeuti's quantum set theory to satisfy De Morgan's lawshttps://zbmath.org/1541.031852024-09-27T17:47:02.548271Z"Ozawa, Masanao"https://zbmath.org/authors/?q=ai:ozawa.masanaoSummary: In [\textit{G. Takeuti}, ``Quantum set theory'', in: E. G. Beltrametti (ed.) and B. C. van Fraassen (ed.), Current issues in quantum logic. Proceedings of the workshop on quantum logic. New York, NY: Springer. 303--322 (1981; \url{doi:10.1007/978-1-4613-3228-2_19})], Takeuti introduced set theory based on quantum logic by constructing a model analogous to Boolean-valued models for Boolean logic. He defined the quantum logical truth value for every sentence of set theory. He showed that equality axioms do not hold, while axioms of ZFC set theory hold if appropriately modified with the notion of commutators. Here, we consider the problem in Takeuti's quantum set theory that De Morgan's laws do not hold for bounded quantifiers. We construct a counter-example to De Morgan's laws for bounded quantifiers in Takeuti's quantum set theory. We redefine the truth value for the membership relation and bounded existential quantification to ensure that De Morgan's laws hold. Then, we show that the truth value of every theorem of ZFC set theory is lower bounded by the commutator of constants therein as quantum transfer principle.
For the entire collection see [Zbl 1479.03003].A degree reduction method for an efficient QUBO formulation for the graph coloring problemhttps://zbmath.org/1541.050642024-09-27T17:47:02.548271Z"Kang, Hyosang"https://zbmath.org/authors/?q=ai:kang.hyosang"Jung, Hyunwoo"https://zbmath.org/authors/?q=ai:jung.hyunwoo"Seol, Chaehwan"https://zbmath.org/authors/?q=ai:seol.chaehwan"Hong, Namho"https://zbmath.org/authors/?q=ai:hong.namho"Lim, Hyunjin"https://zbmath.org/authors/?q=ai:lim.hyunjin"Um, Seokhyun"https://zbmath.org/authors/?q=ai:um.seokhyunSummary: We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.Algorithm for differential equations for Feynman integrals in general dimensionshttps://zbmath.org/1541.140142024-09-27T17:47:02.548271Z"de la Cruz, Leonardo"https://zbmath.org/authors/?q=ai:de-la-cruz.leonardo-r"Vanhove, Pierre"https://zbmath.org/authors/?q=ai:vanhove.pierreFeynman integrals are key ingredients in various areas of physics, and their accurate calculation, whether analytically or numerically, remains a significant hurdle in advancing our understanding of physical phenomena. In particular, identifying the specific types of special functions required to evaluate Feynman integrals has been an ongoing challenge since the early days of quantum field theory.
The authors present an analgorithm for determining the minimal order differential equations associated with a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted to the case of twisted differential forms. In dimensional regularisation, the author proves the applicability of this algorithm by explicitly providing the inhomogeneous differential equations for the multi-loop two-point sunset integrals: up to 20 loops for the equal mass case, the generic mass case at two- and three-loop orders. The authors derive the differential operators for various infrared-divergent two-loop graphs. In the analytic regularisation case, they apply the algorithm for deriving a system of partial differential equations for regulated Witten diagrams, which arise in the evaluation of cosmological correlators of conformally coupled \(\phi^4\) theory in four-dimensional de Sitter space.
Reviewer: Vladimir P. Kostov (Nice)The supergeometric algebra as the language of physicshttps://zbmath.org/1541.150282024-09-27T17:47:02.548271Z"Hamilton, Andrew J. S."https://zbmath.org/authors/?q=ai:hamilton.andrew-j-sSummary: It is shown how the fermions and forces of Nature fit elegantly into the Supergeometric Algebra in 11+1 spacetime dimensions.
For the entire collection see [Zbl 1539.68035].Quantum register algebra: the basic conceptshttps://zbmath.org/1541.150312024-09-27T17:47:02.548271Z"Hrdina, J."https://zbmath.org/authors/?q=ai:hrdina.jaroslav"Hildenbrand, D."https://zbmath.org/authors/?q=ai:hildenbrand.dietmar"Návrat, A."https://zbmath.org/authors/?q=ai:navrat.ales"Steinmetz, C."https://zbmath.org/authors/?q=ai:steinmetz.christian"Alves, R."https://zbmath.org/authors/?q=ai:alves.rafael"Lavor, C."https://zbmath.org/authors/?q=ai:lavor.carlile-campos"Vašík, P."https://zbmath.org/authors/?q=ai:vasik.petr"Eryganov, I."https://zbmath.org/authors/?q=ai:eryganov.ivanSummary: We introduce Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present GAALOP (Geometric Algebra Algorithms Optimizer) implementation of our approach. Using the QRA basis vectors definitions given in Sect. 4 and the framework based on the de Witt basis presented in Sect. 5, we are able to fully describe and compute with QRA in GAALOP using the geometric product. We illustrate the intuitiveness of this computation by presenting the QRA form for the well known SWAP operation on a two qubit register.
For the entire collection see [Zbl 1539.68035].Geometric algebra speaks quantum Esperanto. Ihttps://zbmath.org/1541.150342024-09-27T17:47:02.548271Z"Xambó-Descamps, Sebastian"https://zbmath.org/authors/?q=ai:xambo-descamps.sebastianSummary: The fundamental Stern-Gerlach (SG) experiments suggest that the (pure) states of a \(q\)-bit are the points of the unit sphere \(S^2\) (in some suitable system of units), with a distinguished vector corresponding to the direction of the magnetic field. The goal of this paper is to elucidate the Hermitian structure of the algebra of geometric quaternions \({\mathbf{H}}=\mathcal{G}_3^+\) (that is, the even algebra of the geometric algebra of the Euclidean 3D space) which allows to regard it as the Hilbert space of the \(q\)-bit. The main results are phrased in terms of an explicit \textit{ket map} \(\kappa : \mathbf{H}\rightarrow E_3\) such that \(|\kappa (\mathfrak{q})|=|\mathfrak{q}|\) for all \(\mathfrak{q}\in \mathbf{H} \), and include: that \(\kappa (\mathfrak{q}')=\kappa (\mathfrak{q})\) if and only if \(\mathfrak{q}'\equiv \mathfrak{q} \) (this relation denotes that the two quaternions differ by a phase factor -- a unit \textit{geometric} complex number); that \(\kappa\) is onto; a check that the computed probabilities obey the statistics of the SG experiments; and a recall of the relations between the multiplicative group \(\mathbf{H}^{\times }\) and the rotation group SO \((E_3)\). A sequel paper will explore other facets of the proposed analysis, including the study of the polarization states of electromagnetic waves and more complex spin systems. In conclusion:
\textit{Jes, geometria algebro povas paroli kvantan Esperanton. }
For the entire collection see [Zbl 1539.68035].On the nilpotent orbits arising from admissible affine vertex algebrashttps://zbmath.org/1541.170022024-09-27T17:47:02.548271Z"Arakawa, Tomoyuki"https://zbmath.org/authors/?q=ai:arakawa.tomoyuki"van Ekeren, Jethro"https://zbmath.org/authors/?q=ai:van-ekeren.jethro"Moreau, Anne"https://zbmath.org/authors/?q=ai:moreau.anneThe paper under review provides a simple description, in terms of primitive ideals, of the closure of the nilpotent orbits appearing as associated varieties of admissible affine vertex algebras. The proof uses the representation theory of admissible affine vertex algebras and also dimension counting arguments.
Reviewer: Volodymyr Mazorchuk (Uppsala)On free field realization of quantum affine \(W\)-algebrashttps://zbmath.org/1541.170132024-09-27T17:47:02.548271Z"Kac, Victor G."https://zbmath.org/authors/?q=ai:kac.victor-g"Wakimoto, Minoru"https://zbmath.org/authors/?q=ai:wakimoto.minoruQuantum affine W-algebras are an imporant source of interesting vertex operator algebras constructed from affine Lie algebras. Their construction as cohomolgies of certain complexes is elegant and gives them many interesting links to algebraic geometry, however, it also comes with the drawback that basic algebraic properties such as generators and relations can be hard to access.
This paper aims to solve this problem by constructing certain important generators within a free field realisation. The main formulae for these generators are stated in Theorems 3.1 and 3.2 with the remainder of the paper dedicated to proving these and providing key examples.
Reviewer: Simon Wood (Cardiff)Rationality and fusion rules of exceptional \(\mathcal{W}\)-algebrashttps://zbmath.org/1541.170142024-09-27T17:47:02.548271Z"Arakawa, Tomoyuki"https://zbmath.org/authors/?q=ai:arakawa.tomoyuki"van Ekeren, Jethro"https://zbmath.org/authors/?q=ai:van-ekeren.jethroVertex algebras axiomatise the chiral algebra of 2-dimensional conformal field theories in physics. This paper is concerned with a special class of vertex algebras called \(\mathcal{W}\)-algebras. They are obtained by quantum Hamiltonian reduction of affine vertex algebras and play an important role for integrable models, the geometric Langlands programme, the 4d/2d correspondence and invariants of 4-manifolds.
More concretely, for (some subclass of) the so-called \textit{exceptional} affine \(\mathcal{W}\)-algebras, the authors
(1) prove the modular invariance of characters,
(2) show the rationality and
(3) compute the \(S\)- and \(T\)-matrix and fusion rules.
In fact, they more generally consider lisse \(\mathcal{W}\)-algebras corresponding to admissible affine vertex algebras.
The universal affine \(\mathcal{W}\)-algebra \(\mathcal{W}^k(\mathfrak{g},f)\) is defined by quantum Hamiltonian reduction (or quantised Drinfeld-Sokolov reduction) of the universal affine vertex algebra \(V^k(\mathfrak{g})\) and depends on a finite-dimensional simple Lie algebra \(\mathfrak{g}\), a nilpotent element \(f\in\mathfrak{g}\) and a level \(k\in\mathbb{C}\). The simple affine \(\mathcal{W}\)-algebra \(\mathcal{W}_k(\mathfrak{g},f)\) is defined as the simple quotient of the universal one.
For certain values of \(f\) and \(g\), the simple affine \(\mathcal{W}\)-algebra \(\mathcal{W}_k(\mathfrak{g},f)\) is believed to be rational and lisse (or \(C_2\)-cofinite), meaning that \(\mathcal{W}_k(\mathfrak{g},f)\) and its representation theory are quite well-behaved. For instance, for so-called \textit{admissible} levels \(k=-h^\vee+p/q\) and a nilpotent element \(f\in\mathfrak{g}\) such that \((f,q)\) forms an \textit{exceptional pair}, Kac and Wakimoto conjectured that \(\mathcal{W}_k(\mathfrak{g},f)\) is rational.
The present work considers a generalisation of the notion of \textit{exceptional pair} to the situation where \(f\) lies in the closure of a certain nilpotent orbit \(\mathbb{O}_q\subseteq\mathfrak{g}\), which is the associated variety of the simple affine vertex algebra \(V_k(\mathfrak{g})\). It was conjectured by Arakawa that even all exceptional \(\mathcal{W}\)-algebras \(\mathcal{W}_k(\mathfrak{g},f)\) in this broader sense are rational.
The first main theorem establishes a certain kind of modular invariance result for these exceptional \(\mathcal{W}\)-algebras, lending strong evidence to the rationality conjecture.
The second main result establishes rationality and lissety for a subset of exceptional \(\mathcal{W}\)-algebras for which a certain (somewhat technical) integrability condition relative to \(f\) is satisfied. Morover, the (finitely many) irreducible \(\mathcal{W}_k(\mathfrak{g},f)\)-modules are described as arising from level-\(k\) admissible \(\hat{\mathfrak{g}}\)-modules. As a special case, this result shows the Kac-Wakimoto rationality conjecture for all (in the narrower sense) exceptional \(\mathcal{W}\)-algebras of type \(A\) as well as for the (in the broader sense) exceptional subregular \(\mathcal{W}\)-algebras in simply laced types.
Finally, by the well-known result of Huang, the representation categories of the vertex algebras in the second main theorem provide examples of modular tensor categories. For some cases, the authors compute the modular \(S\)-matrix and the fusion rules. Often, these rational \(\mathcal{W}\)-algebras are not unitary.
Reviewer: Sven Möller (Piscataway)Pseudomodes for biharmonic operators with complex potentialshttps://zbmath.org/1541.341022024-09-27T17:47:02.548271Z"Duc, Tho Nguyen"https://zbmath.org/authors/?q=ai:duc.tho-nguyenSummary: This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This is a newly discovered systematic method that goes beyond the standard semiclassical setting which is a direct consequence. This approach can cover a wide class of previously inaccessible potentials, from logarithmic to superexponential ones.Semiregular non-commutative harmonic oscillators: some spectral asymptotic propertieshttps://zbmath.org/1541.353282024-09-27T17:47:02.548271Z"Malagutti, Marcello"https://zbmath.org/authors/?q=ai:malagutti.marcello"Parmeggiani, Alberto"https://zbmath.org/authors/?q=ai:parmeggiani.albertoSummary: The study is devoted to spectral analysis of systems of PDEs, namely, a class of systems containing certain quantum optics models such as the Jaynes-Cummings model. More in detail, the research deals with spectral Weyl asymptotics for a semiregular system, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch.
For the entire collection see [Zbl 1537.35003].Propagation and energy of the dressed solitons in the Thomas-Fermi magnetoplasmahttps://zbmath.org/1541.353752024-09-27T17:47:02.548271Z"El-Monier, S. Y."https://zbmath.org/authors/?q=ai:el-monier.s-y"Atteya, A."https://zbmath.org/authors/?q=ai:atteya.aSummary: A theoretical investigation is presented for dust-acoustic (DA) waves in a collisionless Thomas-Fermi magnetoplasma. The plasma system consists of electrons, ions, and negatively charged dust grains, all existing in a quantizing magnetic field. The Korteweg-de Vries (KdV) and KdV type equations are derived by using the reductive perturbation method. The solutions of these evolved equations are obtained. The contribution of higher-order corrections to the DA is investigated. The electric field and the soliton energy were also derived. The K-dV and dressed soliton energies are depleted as the dust temperature and magnetic field increase. But they magnify as obliqueness increases. The present results are beneficial in understanding the waves propagating in Thomas-Fermi magnetoplasma that are applicable for high-intensity laser-solid matter interaction experiments and astrophysical compact objects such as white dwarfs.Resonances at the threshold for Pauli operators in dimension twohttps://zbmath.org/1541.354072024-09-27T17:47:02.548271Z"Breuer, Jonathan"https://zbmath.org/authors/?q=ai:breuer.jonathan"Kovařík, Hynek"https://zbmath.org/authors/?q=ai:kovarik.hynekSummary: It is well-known that, due to the interaction between the spin and the magnetic field, the two-dimensional Pauli operator has an eigenvalue 0 at the threshold of its essential spectrum. We show that when perturbed by an effectively positive perturbation, \(V\), coupled with a small parameter \(\varepsilon\), these eigenvalues become resonances. Moreover, we derive explicit expressions for the leading terms of their imaginary parts in the limit \(\varepsilon \searrow 0\). These show, in particular, that the dependence of the imaginary part of the resonances on \(\varepsilon\) is determined by the flux of the magnetic field. The cases of non-degenerate and degenerate zero eigenvalue are treated separately. We also discuss applications of our main results to particles with anomalous magnetic moments.Application of geometric algebra to Koga's work on quantum mechanicshttps://zbmath.org/1541.354082024-09-27T17:47:02.548271Z"Didimos, K. V."https://zbmath.org/authors/?q=ai:didimos.k-vSummary: One of the people who has offered alternatives to the Copenhagen interpretation of quantum mechanics is Toyoki Koga. Some of the important equations in quantum mechanics are the Schrödinger equation, Dirac equation, and Pauli equation; however, Koga only focused on the solutions of the first two. This article briefly introduces geometric algebra to study Koga's works, especially on the Dirac equation and how to get a translation of Koga's solution of the Dirac equation using geometric algebra.
For the entire collection see [Zbl 1531.20003].Nonlinear PDE models in semi-relativistic quantum physicshttps://zbmath.org/1541.354102024-09-27T17:47:02.548271Z"Möller, Jakob"https://zbmath.org/authors/?q=ai:moller.jakob-riishede"Mauser, Norbert J."https://zbmath.org/authors/?q=ai:mauser.norbert-juliusSummary: We present the self-consistent Pauli equation, a semi-relativistic model for charged spin-1/2 particles with self-interaction with the electromagnetic field. The Pauli equation arises as the \(O(1/c)\) approximation of the relativistic Dirac equation. The fully relativistic self-consistent model is the Dirac-Maxwell equation where the description of spin and the magnetic field arises naturally. In the non-relativistic setting, the correct self-consistent equation is the Schrödinger-Poisson equation which does not describe spin and the magnetic field and where the self-interaction is with the electric field only. The Schrödinger-Poisson equation also arises as the mean field limit of the \(N \)-body Schrödinger equation with Coulomb interaction. We propose that the Pauli-Poisson equation arises as the mean field limit \(N\to\infty\) of the linear \(N \)-body Pauli equation with Coulomb interaction where one has to pay extra attention to the fermionic nature of the Pauli equation. We present the semiclassical limit of the Pauli-Poisson equation by the Wigner method to the Vlasov equation with Lorentz force coupled to the Poisson equation which is also consistent with the hierarchy in \(1/c\) of the self-consistent Vlasov equation. This is a non-trivial extension of the groundbreaking works by Lions \& Paul and Markowich \& Mauser, where we need methods like magnetic Lieb-Thirring estimates.Limit behaviors of pseudo-relativistic Hartree equation with power-type perturbationshttps://zbmath.org/1541.354112024-09-27T17:47:02.548271Z"Wang, Qingxuan"https://zbmath.org/authors/?q=ai:wang.qingxuan"Xu, Zefeng"https://zbmath.org/authors/?q=ai:xu.zefengSummary: We consider the following pseudo-relativistic Hartree equations with power-type perturbation,
\[
i \partial_t \psi = \sqrt{- \Delta + m^2} \psi - (\frac{1}{|x|} \ast |\psi|^2) \psi + \varepsilon |\psi|^{p - 2} \psi, \quad \text{with } (t, x) \in \mathbb{R} \times \mathbb{R}^3
\]
where \(2 < p < 3\), \(\varepsilon > 0\) and \(m > 0\), \(p = \frac{8}{3}\) can be viewed as a Slater modification. We mainly focus on the normalized ground state solitary waves \(\varphi_\varepsilon\), where \(\|\varphi_\varepsilon\|_2^2 = N\). Firstly, we prove the existence and nonexistence of normalized ground states under \(L^2\)-subcritical, \(L^2\)-critical \((p = \frac{8}{3})\) and \(L^2\)-supercritical perturbations. Secondly, we classify perturbation limit behaviors of ground states when \(\varepsilon \to 0^+\), and obtain two different blow-up profiles for \(N = N_c\) and \(N > N_c\), where \(N_c\) be regard as ``Chandrasekhar limiting mass''. We prove that \(\langle \varphi_\varepsilon, \sqrt{- \Delta} \varphi_\varepsilon \rangle \sim \varepsilon^{- \frac{2}{3p - 4}}\) for \(N = N_c\) and \(2 < p < 3\), while \(\langle \varphi_\varepsilon, \sqrt{- \Delta} \varphi_\varepsilon \rangle \sim \varepsilon^{- \frac{2}{3p - 8}}\) for \(N > N_c\) and \(\frac{8}{3} < p < 3\). Finally, we study the asymptotic behavior for \(\varepsilon \to + \infty\), and obtain an energy limit \(\lim_{\varepsilon \to + \infty} e_\varepsilon(N) = \frac{1}{2} mN\) and a vanishing rate \(\int_{\mathbb{R}^3} |\varphi_\varepsilon|^p dx \lesssim \varepsilon^{- 1}\) when \(N > N_c\) and \(\frac{8}{3} < p < 3\).Soliton solutions for a quantum particle in one-dimensional boxeshttps://zbmath.org/1541.354132024-09-27T17:47:02.548271Z"Jangid, Anjali"https://zbmath.org/authors/?q=ai:jangid.anjali"Devi, Pooja"https://zbmath.org/authors/?q=ai:devi.pooja"Soni, Harsh"https://zbmath.org/authors/?q=ai:soni.harsh"Chakraborty, Aniruddha"https://zbmath.org/authors/?q=ai:chakraborty.aniruddhaSummary: In this study, we present a new analytical solution for the time-dependent Schrödinger equation for a free particle in one-dimensional case. The solution is derived by doing a non-linear transform to the linear Schrödinger equation and converting it into a Burger-like equation. We obtained an interesting non-stationary wave function where our soliton solution moves in time while maintaining its shape. The new solution is then analysed for three different cases: a periodic box, a box with hard wall boundary conditions and a periodic array of Dirac delta potentials. The resulting analytical solutions exhibit several interesting features including quantized soliton velocity and velocity bands. The analytical soliton solution that has been proposed, in our opinion, makes an important contribution to the study of quantum mechanics and we believe it will contribute significantly to our understanding of how particles behave in one-dimensional box potentials.A weakly turbulent solution to the cubic nonlinear harmonic oscillator on \(\mathbb{R}^2\) perturbed by a real smooth potential decaying to zero at infinityhttps://zbmath.org/1541.354512024-09-27T17:47:02.548271Z"Chabert, Ambre"https://zbmath.org/authors/?q=ai:chabert.ambreSummary: We build a smooth real potential \(V(t, x)\) on \(( t_0,+\infty)\times \mathbb{R}^2\) decaying to zero as \(t\to\infty\) and a smooth solution to the associated perturbed cubic noninear harmonic oscillator whose Sobolev norms blow up logarithmically as \(t\to\infty \). Adapting the method of Faou and Raphael for the linear case, we modulate the Solitons associated to the nonlinear harmonic oscillator by time-dependent parameters solving a quasi-Hamiltonian dynamical system whose action grows up logarithmically, thus yielding logarithmic growth for the Sobolev norm of the solution.Standing waves and global well-posedness for the 2d Hartree equation with a point interactionhttps://zbmath.org/1541.354552024-09-27T17:47:02.548271Z"Georgiev, Vladimir"https://zbmath.org/authors/?q=ai:georgiev.vladimir-s"Michelangeli, Alessandro"https://zbmath.org/authors/?q=ai:michelangeli.alessandro"Scandone, Raffaele"https://zbmath.org/authors/?q=ai:scandone.raffaeleSummary: We study a class of two-dimensional nonlinear Schrödinger equations with point-like singular perturbation and Hartree non-linearity. The point-like singular perturbation of the free Laplacian induces appropriate perturbed Sobolev spaces that are necessary for the study of ground states and evolution flow. We include in our treatment both mass sub-critical and mass critical Hartree non-linearities. Our analysis is two-fold: we establish existence, symmetry, and regularity of ground states, and we demonstrate the well-posedness of the associated Cauchy problem in the singular perturbed energy space. The first goal, unlike other treatments emerging in parallel with the present work, is achieved by a nontrivial adaptation of the standard properties of Schwartz symmetrization for the modified Weinstein functional. This produces, among others, modified Gagliardo-Nirenberg type inequalities that allow to efficiently control the non-linearity and obtain well-posedness by energy methods. The evolution flow is proved to be global in time in the defocusing case, and in the focusing and mass sub-critical case. It is also global in the focusing and mass critical case, for initial data that are suitably small in terms of the best Gagliardo-Nirenberg constant.The large time asymptotic solutions of nonlinear Schrödinger type equationshttps://zbmath.org/1541.354582024-09-27T17:47:02.548271Z"Liu, Baoping"https://zbmath.org/authors/?q=ai:liu.baoping"Soffer, Avy"https://zbmath.org/authors/?q=ai:soffer.avrahamSummary: We give a short description of the proof of asymptotic-completeness for NLS-type equations with radial data in three dimensions. We also show some aspects of the method by giving a new proof of Asymptotic Completeness for the two-body Quantum Scattering case.Stability theory for two-lobe states on the tadpole graph for the NLS equationhttps://zbmath.org/1541.354612024-09-27T17:47:02.548271Z"Pava, Jaime Angulo"https://zbmath.org/authors/?q=ai:angulo-pava.jaimeSummary: The aim of this work is to present new spectral tools for studying the orbital stability of standing waves solutions for the nonlinear Schrödinger equation (NLS) with power nonlinearity on a tadpole graph, namely, a graph consisting of a circle with a half-line attached at a single vertex. By considering \(\delta\)-type boundary conditions at the junction and bound states with a positive two-lobe profile, the main novelty of this paper is at least twofold. Via a splitting eigenvalue method developed by the author, we identify the Morse index and the nullity index of a specific linearized operator around of an \textit{a priori} positive two-lobe state profile for every positive power; and we also obtain new results about the existence and the orbital stability of positive two-lobe states at least in the cubic NLS case. To our knowledge, the results contained in this paper are the first in studying positive bound states for the NLS on a tadpole graph by non-variational techniques. In particular, our approach has prospect of being extended to study stability properties of other bound states for the NLS on a tadpole graph or on other non-compact metric graph such as a looping edge graph, as well as, for other nonlinear evolution models on a tadpole graph.
{{\copyright} 2024 IOP Publishing Ltd \& London Mathematical Society}Multi-fold binary Darboux transformation and mixed solitons of a three-component Gross-Pitaevskii system in the spinor Bose-Einstein condensatehttps://zbmath.org/1541.354712024-09-27T17:47:02.548271Z"Zhang, C.-R."https://zbmath.org/authors/?q=ai:zhang.cairong|zhang.chuanrong|zhang.chunrui|zhang.chunru|zhang.chaoran|zhang.canrong|zhang.chunrui.1|zhang.chenrui|zhang.changrong|zhang.chaorui|zhang.chen-rong|zhang.chengzhao-richard|zhang.chengrui|zhang.changrui"Tian, B."https://zbmath.org/authors/?q=ai:tian.baochuan|tian.bao|tian.bo|tian.baoxian|tian.baolin|tian.baoguang|tian.boping|tian.baofeng|tian.baijun|tian.binbin|tian.beping|tian.baoyu|tian.bailing|tian.baoyuang|tian.baodan|tian.baoping|tian.bin|tian.beiyi|tian.boshi|tian.beihang|tian.boyu|tian.baoguo|tian.bing|tian.baoliang|tian.bowen"Qu, Q.-X."https://zbmath.org/authors/?q=ai:qu.qiuxia|qu.qixing"Yuan, Y.-Q."https://zbmath.org/authors/?q=ai:yuan.yin-quan|yuan.yu-qiang|yuan.yeqing|yuan.yu-quan"Wei, C.-C."https://zbmath.org/authors/?q=ai:wei.cheng-cheng|wei.changcheng|wei.chin-chung|wei.chia-chen|wei.chongchong|wei.chiu-chiSummary: The Bose-Einstein-condensation applications give rise to the superfluidity in the liquid helium and superconductivity in the metals. In this paper, we work on a three-component Gross-Pitaevskii system, which describes the matter waves in an spin-1 spinor Bose-Einstein condensate. We construct a multi-fold binary Darboux transformation with the zero seed solutions to describe the three vertical spin projection of the spin-1 spinor BEC, which is different from all the existing Darboux-type ones for the same system, and derive three types of the exponential-and-rational mixed soliton solutions associated with two conjugate complex eigenvalues. For such mixed solitons, we give their asymptotic expressions, indicating that they consist of the Ieda-Miyakawa-Wadati (IMW)-polar-state or IMW-ferromagnetic solitons but possess the time-dependent velocities. Asymptotically and graphically, interaction mechanisms between the mixed and exponential solitons are classified in six cases, and we exhibit the inelastic and elastic interactions through calculating the modifications of the polarization matrices and phase shifts for the two interacting solitons. We find that both the IMW-polar-state solitons, including the mixed and exponential solitons, can not alter the other soliton's intensity distribution during the interaction, while the mixed or exponential soliton in the IMW-ferromagnetic state does.The formation of invariant exact optical soliton solutions of Landau-Ginzburg-Higgs equation via Khater analytical approachhttps://zbmath.org/1541.354742024-09-27T17:47:02.548271Z"Faridi, Waqas Ali"https://zbmath.org/authors/?q=ai:faridi.waqas-ali"AlQahtani, Salman A."https://zbmath.org/authors/?q=ai:al-qahtani.salman-aSummary: This work aims to enhance our comprehension of the dynamical features of the nonlinear Landau-Ginzburg-Higgs evolution equation, which provides a theoretical framework for identifying various phenomena, such as the formation of superconducting states and the spontaneous breakdown of symmetries. When symmetry breaking is involved in phase transitions in particle physics or condensed matter systems, the Landau-Ginzburg-Higgs model combines the ideas of the Landau-Ginzburg theory and the Higgs mechanism. The equation plays a crucial role in characterizing the Higgs field and its related particles, including Higgs boson. In a standard model of the particle physics, Higgs mechanism explains precisely how mass is acquired. The Lie invariance requirements are taken into account by the symmetry generators. The method produces a 3-dimensional Lie algebra of the Landau-Ginzburg-Higgs model with translational symmetry (dilation or scaling) and translations in the space and the time associated with the mass and energy conservation. It is shown to be the optimal sub-algebraic system after similarity reductions are also performed. The next wave transformation method reduces the governing system to ordinary differential equations and yields a large number of exact travelling wave solutions. The Khater approach is used to solve an ordinary differential equation and investigate the closed-form analytical travelling wave solutions for the considered diffusive system. The obtained results include a singular, mixed singular, periodic, mixed trigonometric, complex combo, trigonometric, mixed hyperbolic, plane, and combined bright-dark soliton solution. The results of the sensitivity analysis demonstrate how vulnerable the suggested equation is to various initial conditions. The findings are visually displayed in contour, three-dimensional, and two-dimensional forms to emphasize the features of pulse propagation.Long time gyrokinetic equationshttps://zbmath.org/1541.354772024-09-27T17:47:02.548271Z"Cheverry, Christophe"https://zbmath.org/authors/?q=ai:cheverry.christophe"Farhat, Shahnaz"https://zbmath.org/authors/?q=ai:farhat.shahnazSummary: The aim of this text is to elucidate the oscillating patterns
(see [\textit{C. Cheverry}, ``Mathematical perspectives in plasma turbulence'', Res. Rep. Math. 2, No. 2 (2018), see also \url{HAL:hal-01617652}])
which are generated in a toroidal plasma by a strong external magnetic field and a nonzero electric field. It is also to justify and then study new modulation equations which are valid for longer times than before. Oscillating coherent structures are induced by the collective motions of charged particles which satisfy a system of ODEs implying a large parameter, the gyrofrequency \(\varepsilon^{-1}\gg 1\). By exploiting the properties of underlying integrable systems, we can complement the KAM picture
(see [\textit{G. Benettin} and \textit{P. Sempio}, Nonlinearity 7, No. 1, 281--303 (1994; Zbl 0856.70010);
\textit{M. Braun}, SIAM Rev. 23, 61--93 (1981; Zbl 0479.76128)])
and go beyond the classical results about gyrokinetics
(see [\textit{M. Bostan}, Multiscale Model. Simul. 8, No. 5, 1923--1957 (2010; Zbl 1220.35176);
\textit{A. J. Brizard} and \textit{T. S. Hahm}, Rev. Mod. Phys. 79, No. 2, 421--468 (2007; Zbl 1205.76309)]).
The purely magnetic situation was addressed by
\textit{C. Cheverry} [Commun. Math. Phys. 338, No. 2, 641--703 (2015; Zbl 1333.35290); J. Differ. Equations 262, No. 3, 2987--3033 (2017; Zbl 1358.35194)].
We are concerned here with the numerous additional difficulties due to the influence of a nonzero electric field.Invariant Gibbs measures for the three dimensional cubic nonlinear wave equationhttps://zbmath.org/1541.355022024-09-27T17:47:02.548271Z"Bringmann, Bjoern"https://zbmath.org/authors/?q=ai:bringmann.bjorn"Deng, Yu"https://zbmath.org/authors/?q=ai:deng.yu"Nahmod, Andrea R."https://zbmath.org/authors/?q=ai:nahmod.andrea-r"Yue, Haitian"https://zbmath.org/authors/?q=ai:yue.haitianSummary: We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic \(\Phi^4_3\)-model. This result is the hyperbolic counterpart to seminal works on the parabolic \(\Phi^4_3\)-model by \textit{M. Hairer} [Invent. Math. 198, No. 2, 269--504 (2014; Zbl 1332.60093)] and \textit{M. Hairer} and \textit{K. Matetski} [Ann. Probab. 46, No. 3, 1651--1709 (2018; Zbl 1406.60094)].
The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates.
The singularity of the Gibbs measure with respect to the Gaussian free field brings out a new caloric representation of the Gibbs measure and a synergy between the parabolic and hyperbolic theories embodied in the analysis of heat-wave stochastic objects. Furthermore from a purely hyperbolic standpoint our argument relies on key new ingredients that include a hidden cancellation between sextic stochastic objects and a new bilinear random tensor estimate.Soliton based director deformation in a twist grain boundary liquid crystalhttps://zbmath.org/1541.355062024-09-27T17:47:02.548271Z"Saravanan, M."https://zbmath.org/authors/?q=ai:saravanan.moorthi"Senjudarvannan, R."https://zbmath.org/authors/?q=ai:senjudarvannan.rSummary: We investigate the director dynamics of a twist grain boundary liquid crystal under the one constant approximation for the different elastic constants representing the various deformation present in the liquid crystal medium. The free energy density is deduced to a higher-order vector nonlinear partial differential equation by balancing the torque experienced by the nematic molecules under a viscous field and the molecular field arises due to the presence of elastic constants. Upon employing the stereographic projection method we further reduced the vector nonlinear differential equation into a complex scalar nonlinear partial differential equation. We obtain a series of localized solutions for the complex scalar nonlinear partial differential equation through the standard tanh method.Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentialshttps://zbmath.org/1541.355072024-09-27T17:47:02.548271Z"Song, Jin"https://zbmath.org/authors/?q=ai:song.jin"Yan, Zhenya"https://zbmath.org/authors/?q=ai:yan.zhenya(no abstract)Matrix representation of magnetic pseudo-differential operators via tight Gabor frameshttps://zbmath.org/1541.355782024-09-27T17:47:02.548271Z"Cornean, Horia D."https://zbmath.org/authors/?q=ai:cornean.horia-d"Helffer, Bernard"https://zbmath.org/authors/?q=ai:helffer.bernard"Purice, Radu"https://zbmath.org/authors/?q=ai:purice.raduSummary: In this paper we use some ideas from
[\textit{H. G. Feichtinger} and \textit{K. Gröchenig}, J. Funct. Anal. 146, No. 2, 464--495 (1997; Zbl 0887.46017);
\textit{K. Gröchenig}, Rev. Mat. Iberoam. 22, No. 2, 703--724 (2006; Zbl 1127.35089)]
and consider the description of Hörmander type pseudo-differential operators on \(\mathbb{R}^d\) (\(d \geq 1\)), including the case of the magnetic pseudo-differential operators introduced in
[\textit{V. Iftimie} et al., Publ. Res. Inst. Math. Sci. 43, No. 3, 585--623 (2007; Zbl 1165.35056);
Rev. Roum. Math. Pures Appl. 64, No. 2--3, 197--223 (2019; Zbl 1463.35517)],
with respect to a tight Gabor frame. We show that all these operators can be identified with some infinitely dimensional matrices whose elements are strongly localized near the diagonal. Using this matrix representation, one can give short and elegant proofs to classical results like the Calderón-Vaillancourt theorem and Beals' commutator criterion, and also establish local trace-class criteria.Macroscopic limits of chaotic eigenfunctionshttps://zbmath.org/1541.370382024-09-27T17:47:02.548271Z"Dyatlov, Semyon"https://zbmath.org/authors/?q=ai:dyatlov.semyonSummary: We give an overview of the interplay between the behavior of high energy eigenfunctions of the Laplacian on a compact Riemannian manifold and the dynamical properties of the geodesic flow on that manifold. This includes the Quantum Ergodicity theorem, the Quantum Unique Ergodicity conjecture, entropy bounds, and uniform lower bounds on mass of eigenfunctions. The above results belong to the domain of \textit{quantum chaos} and use \textit{microlocal analysis}, which is a theory behind the classical/quantum, or particle/wave, correspondence in physics. We also discuss the toy model of quantum cat maps and the challenges it poses for Quantum Unique Ergodicity.
For the entire collection see [Zbl 1532.00039].Higher derivative Hamiltonians with benign ghosts from affine Toda latticeshttps://zbmath.org/1541.370742024-09-27T17:47:02.548271Z"Fring, Andreas"https://zbmath.org/authors/?q=ai:fring.andreas"Turner, Bethan"https://zbmath.org/authors/?q=ai:turner.bethanSummary: We provide further evidence for \textit{A. V. Smilga}'s conjecture [Phys. Lett., A 389, Article ID 127104, 6 p. (2021; Zbl 1485.37055)]
that higher charges of integrable systems are suitable candidates for higher derivative theories that possess benign ghost sectors in their parameter space. As concrete examples we study the properties of the classical phase spaces for a number of affine Toda lattices theories related to different types of Kac-Moody algebras. We identify several types of scenarios for theories with higher charge Hamiltonians: some that possess oscillatory, divergent, benign oscillatory and benign divergent behaviour when ghost sectors are present in the quantum theory. No divergent behaviour was observed for which the trajectories reach a singularity in finite time. For theories based on particular representations for the Lie algebraic roots we found an extreme sensitivity towards the initial conditions governed by the Poisson bracket relations between the centre-of-mass coordinate and the charges.Numerical study of transient Wigner-Poisson model for RTDs: numerical method and its applicationshttps://zbmath.org/1541.651212024-09-27T17:47:02.548271Z"Jiang, Haiyan"https://zbmath.org/authors/?q=ai:jiang.haiyan"Lu, Tiao"https://zbmath.org/authors/?q=ai:lu.tiao"Yao, Wenqi"https://zbmath.org/authors/?q=ai:yao.wenqi"Zhang, Weitong"https://zbmath.org/authors/?q=ai:zhang.weitongSummary: The system of transient Wigner-Poisson equations (TWPEs) is a common model to describe carrier transport in quantum devices. In this paper, we design a second-order semi-implicit time integration scheme for TWPEs with the inflow boundary conditions, and a hybrid sinc-Galerkin/finite-difference method [\textit{H. Jiang} et al., J. Comput. Appl. Math. 409, Article ID 114152, 12 p. (2022; Zbl 1487.81086)] is applied for the spatial discretization. The fully-discretized system is rigorously proved to be unconditionally \(L^2\)-stable, and the computational cost is comparable with that of the second-order explicit Runge-Kutta scheme (ERK2). The numerical method is applied to study a double-barrier resonant tunneling diode (RTD), where representative characteristics of RTDs, including the resonant tunneling effect, bistability and the intrinsic high-frequency current oscillation, are simulated successfully.Foundations of quantum programminghttps://zbmath.org/1541.680052024-09-27T17:47:02.548271Z"Ying, Mingsheng"https://zbmath.org/authors/?q=ai:ying.mingshengPublisher's description: Foundations of Quantum Programming, Second Edition provides a systematic exposition of the subject of quantum programming. Emphasis is placed on foundational concepts, methods, and techniques that can be widely used for various quantum programming models and languages. The book describes how programming methodologies developed for current computers can be extended for quantum computers, along with new programming methodologies that can effectively exploit the unique power of quantum computing. In addition, this resource introduces a chain of quantum programming models from sequential to parallel and distributed programming in the paradigm of superposition-of-data to the paradigm of superposition-of-programs.
Final content presents a series of logical and mathematical tools for verification and analysis of quantum programs, including invariant generation, termination analysis, and abstract interpretation.Type-safe quantum programming in Idrishttps://zbmath.org/1541.680932024-09-27T17:47:02.548271Z"Dandy, Liliane-Joy"https://zbmath.org/authors/?q=ai:dandy.liliane-joy"Jeandel, Emmanuel"https://zbmath.org/authors/?q=ai:jeandel.emmanuel"Zamdzhiev, Vladimir"https://zbmath.org/authors/?q=ai:zamdzhiev.vladimirSummary: Variational Quantum Algorithms are hybrid classical-quantum algorithms where classical and quantum computation work in tandem to solve computational problems. These algorithms create interesting challenges for the design of suitable programming languages. In this paper we introduce Qimaera, which is a set of libraries for the Idris 2 programming language that enable the programmer to implement hybrid classical-quantum algorithms where the full power of the elegant Idris language works in synchrony with quantum programming primitives. The two key ingredients of Idris that make this possible are (1) dependent types which allow us to implement unitary quantum operations; and (2) linearity which allows us to enforce fine-grained control over the execution of quantum operations so that we may detect and reject many physically inadmissible programs. We also show that Qimaera is suitable for variational quantum programming by providing implementations of two prominent variational quantum algorithms -- QAOA and VQE.
For the entire collection see [Zbl 1524.68009].Quantum distinguishing complexity, zero-error algorithms, and statistical zero knowledgehttps://zbmath.org/1541.681472024-09-27T17:47:02.548271Z"Ben-David, Shalev"https://zbmath.org/authors/?q=ai:ben-david.shalev"Kothari, Robin"https://zbmath.org/authors/?q=ai:kothari.robinSummary: We define a new query measure we call quantum distinguishing complexity, denoted \(\operatorname{QD}(f)\) for a Boolean function \(f\). Unlike a quantum query algorithm, which must output a state close to \(|0\rangle\) on a \(0\)-input and a state close to \(|1\rangle\) on a \(1\)-input, a ``quantum distinguishing algorithm'' can output any state, as long as the output states for any \(0\)-input and \(1\)-input are distinguishable.\par Using this measure, we establish a new relationship in query complexity: For all total functions \(f\), \(\operatorname{Q}_0(f)=\widetilde{O}(\operatorname{Q}(f)^5)\), where \(\operatorname{Q}_0(f)\) and \(\operatorname{Q}(f)\) denote the zero-error and bounded-error quantum query complexity of \(f\) respectively, improving on the previously known sixth power relationship.
\par We also define a query measure based on quantum statistical zero-knowledge proofs, \(\operatorname{QSZK}(f)\), which is at most \(\operatorname{Q}(f)\). We show that \(\operatorname{QD}(f)\) in fact lower bounds \(\operatorname{QSZK}(f)\) and not just \(\operatorname{Q}(f)\). \(\operatorname{QD}(f)\) also upper bounds the (positive-weights) adversary bound, which yields the following relationships for all \(f:\operatorname{Q}(f)\ge\operatorname{QSZK}(f)\ge\operatorname{QD}(f)= \Omega(\operatorname{Adv}(f))\). This sheds some light on why the adversary bound proves suboptimal bounds for problems like Collision and Set Equality, which have low QSZK complexity.
\par Lastly, we show implications for lifting theorems in communication complexity. We show that a general lifting theorem for either zero-error quantum query complexity or for QSZK would imply a general lifting theorem for bounded-error quantum query complexity.
For the entire collection see [Zbl 1414.68010].Expressing power of elementary quantum recursion schemes for quantum logarithmic-time computabilityhttps://zbmath.org/1541.681482024-09-27T17:47:02.548271Z"Yamakami, Tomoyuki"https://zbmath.org/authors/?q=ai:yamakami.tomoyukiSummary: Quantum computing has been studied over the past four decades based on two computational models of quantum circuits and quantum Turing machines. To capture quantum polynomial-time computability, a new recursion-theoretic approach was taken lately by \textit{T. Yamakami} [J. Symb. Log. 85, No. 4, 1546--1587 (2020; Zbl 1461.81020)] by way of schematic definitions, which constitute a few initial quantum functions and a few construction schemes, including composition, branching, and multi-qubit quantum recursion. By taking a similar step, we look into quantum logarithmic-time computability and further explore the expressing power of elementary schemes designed for such quantum computation. In particular, we introduce an elementary form of the quantum recursion, called the fast quantum recursion, which helps us capture quantum logarithmic-time computability.
For the entire collection see [Zbl 1511.03002].Acceptance ambiguity for quantum automatahttps://zbmath.org/1541.681862024-09-27T17:47:02.548271Z"Bell, Paul C."https://zbmath.org/authors/?q=ai:bell.paul-c"Hirvensalo, Mika"https://zbmath.org/authors/?q=ai:hirvensalo.mikaSummary: We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA) [\textit{C. Moore} and \textit{J. P. Crutchfield}, Theor. Comput. Sci. 237, No. 1--2, 275--306 (2000; Zbl 0939.68037)]. We study the distribution of acceptance probabilities of such MO-QFA, which is partly motivated by similar freeness problems for matrix semigroups and other computational models. We show that determining if the acceptance probabilities of all possible input words are unique is undecidable for 32 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial configuration is defined over real algebraic numbers. We utilize properties of the skew field of quaternions, free rotation groups, representations of tuples of rationals as a linear sum of radicals and a reduction of the mixed modification Post's correspondence problem.
For the entire collection see [Zbl 1423.68036].Branching bisimulation semantics for quantum processeshttps://zbmath.org/1541.682622024-09-27T17:47:02.548271Z"Wu, Hao"https://zbmath.org/authors/?q=ai:wu.hao.7|wu.hao.3|wu.hao.2|wu.hao.1|wu.hao.14|wu.hao.13|wu.hao|wu.hao.15|wu.hao.6|wu.hao.4|wu.hao.8|wu.hao.17"Yang, Qizhe"https://zbmath.org/authors/?q=ai:yang.qizhe"Long, Huan"https://zbmath.org/authors/?q=ai:long.huanSummary: The qCCS model proposed by Feng et al. provides a powerful framework to describe and reason about quantum communication systems that could be entangled with the environment. However, they only studied weak bisimulation semantics. In this paper we propose a new branching bisimilarity for qCCS and show that it is a congruence. The new bisimilarity is based on the concept of \(\epsilon\)-tree and preserves the branching structure of concurrent processes where both quantum and classical components are allowed. Furthermore, we present a polynomial time equivalence checking algorithm for the ground version of our branching bisimilarity.Applications of the quantum algorithm for st-connectivityhttps://zbmath.org/1541.682802024-09-27T17:47:02.548271Z"Delorenzo, Kai"https://zbmath.org/authors/?q=ai:delorenzo.kai"Kimmel, Shelby"https://zbmath.org/authors/?q=ai:kimmel.shelby"Witter, R. Teal"https://zbmath.org/authors/?q=ai:witter.r-tealSummary: We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity. Furthermore, we show that our algorithm for cycle detection has improved performance under the promise of large circuit rank or a small number of edges. We also provide algorithms for detecting even-length cycles and for estimating the circuit rank of a graph. All of our algorithms have logarithmic space complexity.
For the entire collection see [Zbl 1414.68010].Relativistic dynamics of a charged sphere. Updating the Lorentz-Abraham modelhttps://zbmath.org/1541.780022024-09-27T17:47:02.548271Z"Yaghjian, Arthur D."https://zbmath.org/authors/?q=ai:yaghjian.arthur-dThis is the third edition of a monograph on the relativistic classical motion of a surface-charged insulator sphere in an electromagnetic field. The first and the second editions of this book were published in 1992 and 2006, respectively. The current edition, compared to the second one, has been revised and expanded.
The model of a finite-size charged particle discussed in the book is usually known in the literature as the Abraham-Lorentz model of an electron, although for legitimate chronological reasons the author favors using the term ``the Lorentz-Abraham model''. It has its origins in attempts undertaken by Hendrik Lorentz at the end of the 19th century, that is even before the development of the Special Theory of Relativity, to create a mechanical model describing the motion of an electric charge carrier that would be compatible with Maxwell's theory of electromagnetic phenomena. The model, which takes into account the retarded self-interaction of the particle's spatial charge distribution, was then developed further by Lorentz himself, as well as by Max Abraham and by Henri Poincaré. In the period shortly after the birth of the Special Theory of Relativity, some important amendments were made to it primarily by George Schott. Although with the rise of quantum mechanics and then of quantum electrodynamics the model found itself on the sidelines of the mainstream, various aspects of it still receive attention from theoretical physicists. A manifestation of this is the monograph under review.
The book consists of eight chapters of varying lengths, four appendices, a list of references including 116 items, and a fairly detailed subject index.
Chapter 1 defines the Lorentz-Abraham model, outlines its early history, and dwells on main results presented in subsequent parts of the book. In Chapter 2, the Lorentz-Abraham generalization of the Newton's second law of motion under an action of a prescribed external force is given, together with a pertinent power-loss equation. An outline of derivations of both equations is presented in Chapter 3, although for full details the reader is referred to Appendices A and B. The obtained force and power equations are found to be inconsistent. A solution to this puzzle is discussed in Chapter 4. Following an idea of Poincaré, it is shown that to achieve the compatibility of the Lorentz-Abraham model, it is necessary to take into account the internal forces that keep the particle's charge distribution unchanged in its rest frame. Issues concerning the concept of mass and the relationship between its different types are discussed in Chapter 5. Various energy, momentum and stress-tensor issues are then addressed in Chapters 6 and 7.
Almost half of the book's volume is filled with Chapter 8, where analytical and numerical aspects of solving the Lorentz-Abraham equations of motion for several selected forms of external forces are discussed. In particular, the cases of a particle moving in uniform electric or magnetic fields are analyzed. Much space is also devoted to the description of the motion of an electron in a counter-propagating laser beam. This is the only place in the entire book where, albeit very briefly, quantum effects are analyzed.
The book has been carefully edited. In many places, the key equations have been typed both in four-vector and three-vector notations. This will make the content easier to study for readers at different levels of experience in vector and tensor analysis. Another advantage is the consequent use of the International System of Units (SI).
Reviewer: Radosław Szmytkowski (Gdańsk)Implementation of photon partial distinguishability in a quantum optical circuit simulationhttps://zbmath.org/1541.780042024-09-27T17:47:02.548271Z"Osca, Javier"https://zbmath.org/authors/?q=ai:osca.javier"Vala, Jiri"https://zbmath.org/authors/?q=ai:vala.jiriSummary: We are concerned with numerical simulations of quantum optical circuits under certain realistic conditions, specifically that photon quantum states are not perfectly indistinguishable. The partial photon distinguishability presents a serious limitation in implementation of optical quantum information processing. In order to properly assess its effect on quantum information protocols, accurate numerical simulations, which closely emulate quantum circuit operations, are essential. Our specific objective is to provide a computer implementation of the partial photon distinguishability which is in principle applicable to existing simulation techniques used for ideal quantum circuits and which avoids a need for their significant modification. Our approach is based on the Gram-Schmidt orthonormalization process, which is well suited for our purpose. Photonic quantum states are represented by wavepackets which contain information on their time and frequency distributions. In order to account for the partial photon distinguishability, we expand the number of degrees of freedom associated with the circuit operation extending the definition of the photon channels to incorporate wavepacket degrees of freedom. This strategy allows to define delay operations in the same footing as the linear optical elements.Quantum field theory. An introductionhttps://zbmath.org/1541.810012024-09-27T17:47:02.548271Z"Semenoff, Gordon Walter"https://zbmath.org/authors/?q=ai:semenoff.gordon-walterPublisher's description: This book is a pedagogical introduction to quantum field theory, suitable for a students' first exposure to the subject. It assumes a minimal amount of technical background and it is intended to be accessible to a wide audience including students of theoretical and experimental high energy physics, condensed matter, optical, atomic, nuclear and gravitational physics and astrophysics. It includes a thorough development of second quantization and the field theoretic approach to nonrelativistic many-body physics as a step in developing a broad-based working knowledge of the basic aspects of quantum field theory. It presents a logical and systematic first principles development of relativistic field theory and of functional techniques and perturbation theory with Feynman diagrams, renormalization, and basic computations in quantum electrodynamics.Completely discretized, finite quantum mechanicshttps://zbmath.org/1541.810022024-09-27T17:47:02.548271Z"Carroll, Sean M."https://zbmath.org/authors/?q=ai:carroll.sean-mSummary: I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schrödinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.Relaxation to quantum equilibrium and the Born rule in Nelson's stochastic dynamicshttps://zbmath.org/1541.810032024-09-27T17:47:02.548271Z"Hardel, Vincent"https://zbmath.org/authors/?q=ai:hardel.vincent"Hervieux, Paul-Antoine"https://zbmath.org/authors/?q=ai:hervieux.paul-antoine"Manfredi, Giovanni"https://zbmath.org/authors/?q=ai:manfredi.giovanniSummary: Nelson's stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson's stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double slit and harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed \textit{before} the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson's theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production.An alternative foundation of quantum theoryhttps://zbmath.org/1541.810042024-09-27T17:47:02.548271Z"Helland, Inge S."https://zbmath.org/authors/?q=ai:helland.inge-sSummary: A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations.On the modulus duality in arbitrary codimensionhttps://zbmath.org/1541.810052024-09-27T17:47:02.548271Z"Lohvansuu, Atte"https://zbmath.org/authors/?q=ai:lohvansuu.atteSummary: We study the modulus of dual families of \(k\)- and \((n-k)\)-dimensional Lipschitz chains of Euclidean \(n\)-cubes and establish half of the modulus duality identity.On the status of DELL systemshttps://zbmath.org/1541.810062024-09-27T17:47:02.548271Z"Mironov, A."https://zbmath.org/authors/?q=ai:mironov.andrei-d"Morozov, A."https://zbmath.org/authors/?q=ai:morozov.alexei-yurievichSummary: A detailed review of the \(p, q\)-duality for Calogero system and its generalizations is given. For the first time, we present some of elliptic-trigonometric Hamiltonians dual to the elliptic Ruijsenaars Hamiltonians (i.e. trigonometric-elliptic ones), and explain their relations to the bi-elliptic Koroteev-Shakirov (KS) model. The most interesting self-dual double-elliptic (DELL) system remains a mystery, but we provide a clearer formulation of the problem and describe the steps that are still to be done.Large orbits on Markoff-type K3 surfaces over finite fieldshttps://zbmath.org/1541.810072024-09-27T17:47:02.548271Z"O'Dorney, Evan M."https://zbmath.org/authors/?q=ai:odorney.evan-mSummary: We study the surface \(\mathcal{W}_k:x^2+y^2+z^2+x^2y^2z^2 = kxyz\) in \((\mathbb{P}^1)^3\), a tri-involutive K3 (TIK3) surface. We explain a phenomenon noticed by \textit{E. Fuchs} et al. [``Orbits on K3 Surfaces of Markoff Type'', Preprint, \url{arXiv:2201.12588}]: over a finite field of order \(\equiv 1\mod 8\), the points of \(\mathcal{W}_4\) do not form a single large orbit under the group \(\Gamma\) generated by the three involutions fixing two variables and a few other obvious symmetries, but rather admit a partition into two \(\Gamma\)-invariant subsets of roughly equal size. The phenomenon is traced to an explicit double cover of the surface.Does a second-class primary constraint generate a gauge transformation? Electromagnetisms and gravities, massless and massivehttps://zbmath.org/1541.810082024-09-27T17:47:02.548271Z"Pitts, J. Brian"https://zbmath.org/authors/?q=ai:pitts.j-brianSummary: In constrained Hamiltonian dynamics there are two views regarding how first-class constraints generate gauge transformations: individually or only in a certain combination, the Rosenfeld-Anderson-Bergmann-Castellani gauge generator. This gauge generator \(G\) preserves Hamilton's equations and changes the canonical action at most by a boundary term; Hamiltonian's equations are the Euler-Lagrange equations for the canonical action. Hence the canonical formalism is equivalent to the Lagrangian formalism, and indeed subsumed within it (in important examples) with many canonical momenta serving as auxiliary fields. \(G\) generates transformations basically equivalent to the usual 4-dimensional Lagrangian expressions, such as a 4-gradient in electromagnetism or a space-time coordinate transformation (on-shell) in General Relativity. It has been shown recently that separate first-class constraints lead to inequivalent observables between Proca non-gauge and Stueckelberg gauge massive electromagnetism. There is, however, widespread agreement that second-class constraints do not generate gauge transformations.
Here it is shown that in such a sense as the first-class primary constraint in Maxwell's theory generates a gauge transformation, the second-class primary constraint in Proca's massive electromagnetism also generates a gauge transformation. Likewise the second-class primary constraints in various massive spin 2 relatives of General Relativity generate as much of a gauge transformation as do the corresponding first-class primary constraints in GR. Hence the view that first-class constraints typically generate gauge transformations \textit{individually} faces a puzzle not faced by the gauge generator view.On Buschman-Erdelyi and Mehler-Fock transforms related to the group \(SO_0(3,1)\)https://zbmath.org/1541.810092024-09-27T17:47:02.548271Z"Shilin, Il'ya Anatol'evich"https://zbmath.org/authors/?q=ai:shilin.ilya-anatolevichSummary: By using a functional defined on a pair of the assorted represention spaces of the connected subgroup of the proper Lorentz group, a formula for the Buschman-Erdelyi transform of the Legendre function (up to a factor) is derived. Also a formula for the Mehler-Fock transform of the Legendre function of an inverse argument is obtained. Moreover, a generalization of one known formula for the Mehler-Fock transform is derived.Not even 6 dB: Gaussian quantum illumination in thermal backgroundhttps://zbmath.org/1541.810102024-09-27T17:47:02.548271Z"Volkoff, T. J."https://zbmath.org/authors/?q=ai:volkoff.t-jSummary: In analyses of target detection with Gaussian state transmitters in a thermal background, the thermal occupation is taken to depend on the target reflectivity in a way which simplifies the analysis of the symmetric quantum hypothesis testing problem. However, this assumption precludes comparison of target detection performance between an arbitrary transmitter and a vacuum state transmitter, i.e. `detection without illumination', which is relevant in a bright thermal background because a target can be detected by its optical shadow or some other perturbation of the background. Using a target-agnostic thermal environment leads to the result that the oft-claimed 6 dB possible reduction in the quantum Chernoff exponent for a two-mode squeezed vacuum transmitter over a coherent state transmitter in high-occupation thermal background is an unachievable limiting value, only occurring in a limit in which the target detection problem is ill-posed. Further analyzing quantum illumination in a target-agnostic thermal environment shows that a weak single-mode squeezed transmitter performs worse than `no illumination', which is explained by the noise-increasing property of reflected low-intensity squeezed light.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}Some remarks on the notion of transitionhttps://zbmath.org/1541.810112024-09-27T17:47:02.548271Z"Ciaglia, Florio M."https://zbmath.org/authors/?q=ai:ciaglia.florio-maria"Di Cosmo, Fabio"https://zbmath.org/authors/?q=ai:di-cosmo.fabioSummary: In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. We could distinguish between classical probability theory where propositions can be conditioned if they have a non-zero intersection, from cases where ``non-local'' conditioning are allowed. The algebraic and geometrical properties of groupoids can be exploited to construct models of such non-local description.
For the entire collection see [Zbl 1528.53002].A critical analysis of `Relative facts do not exist: relational quantum mechanics is incompatible with quantum mechanics' by Jay Lawrence, Marcin Markiewicz and Marek Żukowskihttps://zbmath.org/1541.810122024-09-27T17:47:02.548271Z"Drezet, Aurélien"https://zbmath.org/authors/?q=ai:drezet.aurelienSummary: We discuss a recent work by \textit{J. Lawrence} et al. [``Relative facts of relational quantum mechanics are incompatible with quantum mechanics'', Preprint, \url{arXiv:2208.11793}] criticizing relational quantum mechanics (RQM) and based on a famous nonlocality theorem Going back to Greenberger Horne and Zeilinger (GHZ). Here, we show that the claims presented in this recent work are unjustified and we debunk the analysis.Quantum theory in finite dimension cannot explain every general process with finite memoryhttps://zbmath.org/1541.810132024-09-27T17:47:02.548271Z"Fanizza, Marco"https://zbmath.org/authors/?q=ai:fanizza.marco"Lumbreras, Josep"https://zbmath.org/authors/?q=ai:lumbreras.josep"Winter, Andreas"https://zbmath.org/authors/?q=ai:winter.andreas-jSummary: Arguably, the largest class of stochastic processes generated by means of a finite memory consists of those that are sequences of observations produced by sequential measurements in a suitable generalized probabilistic theory (GPT). These are constructed from a finite-dimensional memory evolving under a set of possible linear maps, and with probabilities of outcomes determined by linear functions of the memory state. Examples of such models are given by classical hidden Markov processes, where the memory state is a probability distribution, and at each step it evolves according to a non-negative matrix, hidden quantum Markov processes, where the memory is a finite-dimensional quantum system, and at each step is evolves accorading to a completely positive map. Here we show that the set of processes admitting a finite-dimensional explanation do not need to be explainable in terms of either classical probability or quantum mechanics. To wit, we exhibit families of processes that have a finite-dimensional explanation, defined manifestly by th edynamics of an explicitly given GPT, but that do not admit a quantum, and therefore not even classical, explanation in finite dimension. Furthermore, we present a family of quantum processes on qubits and qutrits that do not admit a classical finite-dimensional realization, which includes examples introduced earlier by Fox, Rubin, Dhamardikari and Nadkarni as functions of finite-dimensional Markov chains, and lower bound the size of the memory of a classical model realizing a noisy version of the qubit processes.On the evolution of states in a quantum-mechanical model of experimentshttps://zbmath.org/1541.810142024-09-27T17:47:02.548271Z"Fröhlich, Jürg"https://zbmath.org/authors/?q=ai:frohlich.jurg-martin"Gang, Zhou"https://zbmath.org/authors/?q=ai:gang.zhouSummary: Ideas and results in the quantum theory of experiments are reviewed. To fix ideas, a concrete example of indirect measurements, an experiment devised by \textit{C. Guerlin} et al. [Nature, London 448, No. 7156, 889--893 (2007; \url{doi:10.1038/nature06057})], and theoretical interpretations thereof [\textit{M. Bauer} and \textit{D. Bernard}, Phys. Rev. A (3) 84, No. 4, Article ID 044103, 4 p. (2011; \url{doi:10.1103/PhysRevA.84.044103}); \textit{M. Bauer} et al., Ann. Henri Poincaré 14, No. 4, 639--679 (2013; Zbl 1273.81026)] are recalled. Subsequently two important elements of the Copenhagen interpretation of quantum mechanics, viz. the \textit{von Neumann-} and the \textit{Lüders measurement postulates}, are recalled and rendered more precise. Next, a model originally proposed by \textit{N. Gisin} et al. [Phys. Rev. Lett. 52, No. 19, 1657--1660 (1984; \url{doi:10.1103/PhysRevLett.52.1657})] is described and shown to imply these postulates. It is then used to provide a theoretical description of the experiment in [Guerlin et al., loc. cit.] involving a ``Heisenberg cut'' differing from the one invoked in [Bauer and Bernard, loc. cit.; Bauer et al., loc. cit.; \textit{M. Ballesteros} et al., J. Stat. Phys. 162, No. 4, 924--958 (2016; Zbl 1337.81015)]. Some technical issues in the analysis of Gisin's model [loc. cit.] are elaborated upon. The paper concludes with remarks on a general principle that implies a universal law governing the stochastic time evolution of states of individual physical systems featuring events and leading to a solution of the so-called measurement problem in quantum mechanics.\(q\)-analog qudit Dicke stateshttps://zbmath.org/1541.810152024-09-27T17:47:02.548271Z"Raveh, David"https://zbmath.org/authors/?q=ai:raveh.david"Nepomechie, Rafael I."https://zbmath.org/authors/?q=ai:nepomechie.rafael-iSummary: Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are their \(d\)-level generalization. We define here \(q\)-deformed qudit Dicke states using the quantum algebra \(su_q(d)\). We show that these states can be compactly expressed as a weighted sum over permutations with \(q\)-factors involving the so-called inversion number, an important permutation statistic in Combinatorics. We use this result to compute the bipartite entanglement entropy of these states. We also discuss the preparation of these states on a quantum computer, and show that introducing a \(q\)-dependence does not change the circuit gate count.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}Optimal discrimination of two nonorthogonal states by continuous probing and feedback operationhttps://zbmath.org/1541.810162024-09-27T17:47:02.548271Z"Xu, Peng"https://zbmath.org/authors/?q=ai:xu.peng.5"Zhao, Peng"https://zbmath.org/authors/?q=ai:zhao.peng.2"Zhao, Shengmei"https://zbmath.org/authors/?q=ai:zhao.shengmeiSummary: For a quantum system prepared probabilistically on two or more non-orthogonal states, the observer cannot discriminate the initial preparation perfectly. \textit{K. Jacobs} [Quantum Inf. Comput. 7, No. 1--2, 127--138 (2007; Zbl 1152.81741)] introduced a measurement operator that could increase the rate of information obtained using a continuous measurement scheme. However, the better effect happens at the expense of reducing the total information from the quantum system. To address this problem, an optimal operator that could yield the maximal value of mutual information for a long-time measurement is found. Particularly, it turns out that the error probability is minimized for any measurement moment by measuring the optimal operator. Furthermore, for a given finite measurement time, a measurement scheme to maximize the obtained mutual information is presented. It is shown that while the Jacobs' operator should be used for a short-time case, for a long-time limit, the proposed optimal operator should be employed. For a given finite duration, the proposal could determine the optimal measurement operator that maximizes the final value of mutual information.
{\copyright} 2022 Wiley-VCH GmbHOptimal quantum speed for mixed stateshttps://zbmath.org/1541.810172024-09-27T17:47:02.548271Z"Naderzadeh-ostad, Ashraf"https://zbmath.org/authors/?q=ai:naderzadeh-ostad.ashraf"Akhtarshenas, Seyed Javad"https://zbmath.org/authors/?q=ai:akhtarshenas.seyed-javadSummary: The question of how fast a quantum state can evolve is considered. Using the definition of squared speed based on the Euclidean distance given in [\textit{D. C. Brody} and \textit{B. Longstaff}, Phys. Rev. Res. 1, No. 3, Article ID 033127, 5 p. (2019; \url{doi:10.1103/PhysRevResearch.1.033127})], we present a systematic framework to obtain the optimal speed of a \(d\)-dimensional system evolved unitarily under a time-independent Hamiltonian. Among the set of mixed quantum states having the same purity, the optimal state is obtained in terms of its purity parameter. We show that for an arbitrary \(d\), the optimal state is represented by a \(X\)-state with an additional property of being symmetric with respect to the secondary diagonal. For sufficiently low purities for which the purity exceeds the purity of maximally mixed state \(\mathbb{I}/d\) by at most \(2/d^2\), the only nonzero off-diagonal entry of the optimal state is \(\varrho_{1d}\), corresponding to the transition amplitude between two energy eigenstates with minimum and maximum eigenvalues, respectively. For larger purities, however, whether or not the other secondary diameter entries \(\varrho_{i, d - i + 1}\) take nonzero values depends on their relative energy gaps \(|E_{d-i+1} - E_i|\). The effects of coherence and entanglement, with respect to the energy basis, are also examined and found that for optimal states both resources are monotonic functions of purity, so they can cause speed up quantum evolution leading to a smaller quantum speed limit. Our results show that although the coherence of the states is responsible for the speed of evolution, only the coherence caused by some off-diagonal entries located on the secondary diagonal play a role in the fastest states.
{{\copyright} 2024 IOP Publishing Ltd}Inductive proof of Borchardt's theoremhttps://zbmath.org/1541.810182024-09-27T17:47:02.548271Z"Chavez, Andy A."https://zbmath.org/authors/?q=ai:chavez.andy-a"Adam, Alec P."https://zbmath.org/authors/?q=ai:adam.alec-p"Ayers, Paul W."https://zbmath.org/authors/?q=ai:ayers.paul-w"Miranda-Quintana, Ramón Alain"https://zbmath.org/authors/?q=ai:miranda-quintana.ramon-alainSummary: We provide a (strong) inductive proof of Borchardt's theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and suggests that the restriction of the APIG coefficients to Cauchy form (typically called APr2G) is special in its tractability.The reflected entanglement spectrum for free fermionshttps://zbmath.org/1541.810192024-09-27T17:47:02.548271Z"Dutta, Souvik"https://zbmath.org/authors/?q=ai:dutta.souvik"Faulkner, Thomas"https://zbmath.org/authors/?q=ai:faulkner.thomas"Lin, Simon"https://zbmath.org/authors/?q=ai:lin.simon-c|lin.simon-mSummary: We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.Thread/state correspondence: from bit threads to qubit threadshttps://zbmath.org/1541.810202024-09-27T17:47:02.548271Z"Lin, Yi-Yu"https://zbmath.org/authors/?q=ai:lin.yi-yu"Jin, Jie-Chen"https://zbmath.org/authors/?q=ai:jin.jie-chenSummary: Starting from an interesting coincidence between the bit threads and SS (surface/state) correspondence, both of which are closely related to the holographic RT formula, we introduce a property of bit threads that has not been explicitly proposed before, which can be referred to as thread/state correspondence (see [\textit{Y.-Y. Lin} and \textit{J.-C. Jin}, ``Thread/state correspondence: the qubit threads model of holographic gravity'', Preprint, \url{arXiv:2208.08963}] for a brief pre-release version). Using this thread/state correspondence, we can construct the explicit expressions for the SS states corresponding to a set of bulk extremal surfaces in the SS correspondence, and nicely characterize their entanglement structure. Based on this understanding, we use the locking bit thread configurations to construct a holographic qubit threads model as a new toy model of the holographic principle, and show that it is closely related to the holographic tensor networks, the kinematic space, and the connectivity of spacetime.Nonlocal operation enhanced entanglement detection and classificationhttps://zbmath.org/1541.810212024-09-27T17:47:02.548271Z"Li, Yan"https://zbmath.org/authors/?q=ai:li.yan.80"Ren, Zhihong"https://zbmath.org/authors/?q=ai:ren.zhihongSummary: Based on the nature that nonlocal operation will change the fixed quantum statistical speed limited by the local operation, we study the performance of Ising-type nonlocal operation in multipartite entanglement detection and classification. We first present the formula of quantum statistical speed for general quantum state under the two-body nonlocal operation, and then investigate several important and experimentally relevant states, including \(N\)-qubit W state, Twin-Fock state, Q state and \(N\)-qubit GHZ state. The results show that the optimal nonlocal operation can be used to address some intractable problems encountered under the local operation, such as the classification of \(N\)-qubit W state and entanglement detection of Q state at the edges. Meanwhile, some defects are presented and discussed. Interestingly, the \(N\)-qubit GHZ state is found to be stable when it is probed by weaker nonlocal operation (\(\gamma \leq \sqrt{N-1}\)) and it maybe helpful to the experimental research. Our work provides an alternative route to investigate entanglement detection and classification, especially for the novel and complex quantum system.Classifying the non-time-local and entangling dynamics of an open qubit systemhttps://zbmath.org/1541.810222024-09-27T17:47:02.548271Z"Prudhoe, Sean"https://zbmath.org/authors/?q=ai:prudhoe.sean"Shandera, Sarah"https://zbmath.org/authors/?q=ai:shandera.sarahSummary: We study families of dynamical maps generated from interactions with varying degrees of symmetry. For a family of time-independent Hamiltonians, we demonstrate the relationship between symmetry, strong-coupling, perfect entanglers, non-Markovian features, and non-time-locality. We show that by perturbing the initial environment state, effective time-local descriptions can be obtained that are non-singular yet capture essential non-unitary features of the reduced dynamics. We then consider a time-dependent Hamiltonian that changes the degree of symmetry by activating a dormant degree of freedom. In this example we find that the one-qubit reduced dynamics changes dramatically. These results can inform the construction of effective theories of open systems when the larger system dynamics is unknown.Decoherence as a high-dimensional geometrical phenomenonhttps://zbmath.org/1541.810232024-09-27T17:47:02.548271Z"Soulas, Antoine"https://zbmath.org/authors/?q=ai:soulas.antoineSummary: We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the level of decoherence induced by a purely random environment on a system according to their respectives sizes, and to exhibit some links with entanglement entropy.Coherent states and entropyhttps://zbmath.org/1541.810242024-09-27T17:47:02.548271Z"Barron, Tatyana"https://zbmath.org/authors/?q=ai:barron.tatyana"Kazachek, Alexander"https://zbmath.org/authors/?q=ai:kazachek.alexanderConsider the Kähler manifold \(M\!=\!\mathbb{C}^n\). For \(k\!\in\!\mathbb{N}\) and a point \(p\in M\), the coherent vector defined as
\[
\Theta _p^{(k)}\!:\!M\!\rightarrow\!\mathbb{C}, \Theta _p^{(k)}(z)\!=\!\mathrm{e}^{kz^T\overline{p}},
\]
belongs to the Segal-Bargmann space \(H_k\) of holomorphic functions \(f\!:\!M\!\rightarrow\!\mathbb{C}\) satisfying a certain integrability condition. The authors investigate the entanglement entropy \(E_k(b_k)\) of the Bell-type pure state
\[
b_k\!=\!(1/||w_k||)w_k\in\!H_k\!\otimes\!H_k,
\]
where
\[
w_k=(1/||\Theta_p^{(k)}||^2)\Theta_p^{(k)}\!\otimes \Theta_p^{(k)}+ (1/||\Theta_q^{(k)}||^2)\Theta_q^{(k)}\!\otimes \Theta_q^{(k)}
\]
and \(p,q\!\in\!M\). More exactly, they prove a positive lower bound for \(E_k(b_k)\), asymptotic in \(k\) as \(k\!\rightarrow \!\infty\). By definition,
\[
E_k(b_k)\!=\!-\mathrm{Tr}(\varrho \, \mathrm{ln}\, \varrho),
\]
where \(\varrho\! =\!\mathrm{Tr}_2(P_{b_k})\) and \(P_{b_k}\) is the rank 1 orthogonal projector onto the 1-dimensional linear subspace of \(H_k\!\otimes\!H_k\) spanned by \(b_k\).
The authors also present a version for the case of compact manifolds \(M\).
For the entire collection see [Zbl 1528.94003].
Reviewer: Nicolae Cotfas (Bucureşti)Crossed products, extended phase spaces and the resolution of entanglement singularitieshttps://zbmath.org/1541.810252024-09-27T17:47:02.548271Z"Klinger, Marc S."https://zbmath.org/authors/?q=ai:klinger.marc-s"Leigh, Robert G."https://zbmath.org/authors/?q=ai:leigh.robert-gSummary: We identify a direct correspondence between the crossed product construction which plays a crucial role in the theory of Type III von Neumann algebras, and the extended phase space construction which restores the integrability of non-zero charges generated by gauge symmetries in the presence of spatial substructures. This correspondence provides a blue-print for \textit{resolving} singularities which are encountered in the computation of entanglement entropy for subregions in quantum field theories. The extended phase space encodes quantities that would be regarded as `pure gauge' from the perspective of the full theory, but are nevertheless necessary for gluing together, in a path integral sense, physics in different subregions. These quantities are required in order to maintain gauge covariance under such gluings. The crossed product provides a consistent method for incorporating these necessary degrees of freedom into the operator algebra associated with a given subregion. In this way, the extended phase space completes the subregion algebra and subsequently allows for the assignment of a meaningful, finite entropy to states therein.The entanglement criteria based on equiangular tight frameshttps://zbmath.org/1541.810262024-09-27T17:47:02.548271Z"Shi, Xian"https://zbmath.org/authors/?q=ai:shi.xianSummary: Finite tight frames play an important role in miscellaneous areas, including quantum information theory. Here we apply a class of tight frames, equiangular tight frames, to address the problem of detecting the entanglement of bipartite states. Here we derive some entanglement criteria based on positive operator-valued measurements built from equiangular tight frames. We also present a class of entanglement witnesses based on the equiangular tight frames. At last, we generalize the entanglement criterion for bipartite systems to multipartite systems.
{{\copyright} 2024 IOP Publishing Ltd}Equivariant relative submajorizationhttps://zbmath.org/1541.810272024-09-27T17:47:02.548271Z"Bunth, Gergely"https://zbmath.org/authors/?q=ai:bunth.gergely"Vrana, Péter"https://zbmath.org/authors/?q=ai:vrana.peterEditorial remark: No review copy delivered.Quantum advantage beyond entanglement in Bayesian game theoryhttps://zbmath.org/1541.810282024-09-27T17:47:02.548271Z"Lowe, A."https://zbmath.org/authors/?q=ai:lowe.adam|lowe.andrew|lowe.alexander|lowe.a-jSummary: Quantum discord has been utilised in order to find quantum advantage in an extension of the Clauser, Horne, Shimony, and Holt game [\textit{J. F. Clauser} et al., Phys. Rev. Lett. 23, 880--883 (1969; Zbl 1371.81014)]. By writing the game explicitly as a Bayesian game, the resulting game is modified such the payoff's are different. Crucially, restrictions are imposed on the measurements that Alice and Bob can perform. By imposing these restrictions, it is found that there exists quantum advantage beyond entanglement for a given quantum state. This is shown by decomposing the expected payoff into a classical and quantum term. By optimising over the expected payoff, the classical limit is surpassed for the given state in the restricted measurement space. This gives an operational framework in order to witness and determine the quantum discord for specific states, whilst demonstrating the importance of measurement in quantum advantage.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}A synchronous NPA hierarchy with applicationshttps://zbmath.org/1541.810292024-09-27T17:47:02.548271Z"Russell, Travis B."https://zbmath.org/authors/?q=ai:russell.travis-bSummary: We present an adaptation of the NPA hierarchy to the setting of synchronous correlation matrices. Our adaptation improves upon the original NPA hierarchy by using smaller certificates and fewer constraints, although it can only be applied to certify synchronous correlations. We recover characterizations for the sets of synchronous quantum commuting and synchronous quantum correlations. For applications, we show that the existence of symmetric informationally complete positive operator-valued measures and maximal sets of mutually unbiased bases can be verified or invalidated with only two certificates of our adapted NPA hierarchy.Quantum-mechanical four-body versus semi-classical three-body theories for double charge exchange in collisions of fast alpha particles with helium targetshttps://zbmath.org/1541.810302024-09-27T17:47:02.548271Z"Belkić, Dževad"https://zbmath.org/authors/?q=ai:belkic.dzevadSummary: Within the two-channel distorted wave second-order perturbative theoretical formalism, we study capture of both electrons from helium-like targets by heavy nuclei as projectiles at intermediate and high impact energies. The emphasis is on the four-body single-double scattering (SDS-4B) method and the three-body continuum distorted wave impact parameter method (CDW-3B-IPM). The SDS-4B method deals with the full quantum-mechanical correlative dynamics of all the four interactively participating particles (two electrons, two nuclei). The CDW-3B-IPM is a semi-classical three-body independent particle model (one electron, two nuclei), using a combinatorial calculus to describe double capture by a product of two uncorrelated probabilities, integrated over impact parameters. Both theories share a common feature in having altogether two electronic full Coulomb continuum wave functions. One such function is centered on the projectile nucleus in the entrance channel, whereas the other is centered on the target nucleus in the exit channel. These two methods satisfy the correct initial and final Coulomb boundary conditions in the asymptotic region of scattering, at infinitely large inter-particle separations. Yet, it is presently demonstrated that most of the available experimental data on total cross sections for the double capture from helium by alpha particles distinctly favor the SDS-4B method. This is especially true at intermediate energies. Such energies are critically important in versatile applications under the general umbrella of ion transport in matter, including thermonuclear fusion (plasma physics) and ion therapy (medicine).On channels of energy for the radial linearised energy critical wave equation in the degenerate casehttps://zbmath.org/1541.810312024-09-27T17:47:02.548271Z"Collot, Charles"https://zbmath.org/authors/?q=ai:collot.charles"Duyckaerts, Thomas"https://zbmath.org/authors/?q=ai:duyckaerts.thomas"Kenig, Carlos"https://zbmath.org/authors/?q=ai:kenig.carlos-e"Merle, Frank"https://zbmath.org/authors/?q=ai:merle.frankSummary: Channels of energy estimates control the energy of an initial data from that which it radiates outside a light cone. For the linearised energy critical wave equation, they have been obtained in the radial case in odd dimensions, first in three dimensions in [\textit{T. Duyckaerts} et al., Camb. J. Math. 1, No. 1, 75--144 (2013; Zbl 1308.35143)], then for the general case in [\textit{T. Duyckaerts} et al., Commun. Math. Phys. 379, No. 3, 1113--1175 (2020; Zbl 1450.35157)]. We consider even dimensions, for which such estimates are known to fail [\textit{R. Côte} et al., Math. Ann. 358, No. 3--4, 573--607 (2014; Zbl 1311.35022)]. We propose a weaker version of these estimates, around a single ground state as well as around a multisoliton. This allows us in [\textit{C. Collot} et al., ``Soliton resolution for the radial quadratic wave equation in six space dimensions'', Preprint, \url{arXiv:2201.01848}] to prove the soliton resolution conjecture in six dimensions.Recoverability of quantum channels via hypothesis testinghttps://zbmath.org/1541.810322024-09-27T17:47:02.548271Z"Jenčová, Anna"https://zbmath.org/authors/?q=ai:jencova.annaSummary: A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the channel. Using a new integral representation of the relative entropy in [\textit{P. E. Frenkel}, Quantum 7, Paper No. 1102, 16 p. (2023; \url{doi:10.22331/q-2023-09-07-1102})], we present an easy proof of a characterization of sufficient quantum channels and recoverability by preservation of optimal success probabilities in hypothesis testing problems, equivalently, by preservation of \(L_1\)-distance.Holographic measurement and quantum teleportation in the SYK thermofield doublehttps://zbmath.org/1541.810332024-09-27T17:47:02.548271Z"Antonini, Stefano"https://zbmath.org/authors/?q=ai:antonini.stefano"Grado-White, Brianna"https://zbmath.org/authors/?q=ai:grado-white.brianna"Jian, Shao-Kai"https://zbmath.org/authors/?q=ai:jian.shao-kai"Swingle, Brian"https://zbmath.org/authors/?q=ai:swingle.brian-gSummary: According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the Sachdev-Ye-Kitaev (SYK) model's thermofield double state, dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate the (Renyi-2) mutual information between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the von Neumann entropy. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of traversable wormholes.Topological quantum computation on supersymmetric spin chainshttps://zbmath.org/1541.810342024-09-27T17:47:02.548271Z"Jana, Indrajit"https://zbmath.org/authors/?q=ai:jana.indrajit"Montorsi, Filippo"https://zbmath.org/authors/?q=ai:montorsi.filippo"Padmanabhan, Pramod"https://zbmath.org/authors/?q=ai:padmanabhan.pramod"Trancanelli, Diego"https://zbmath.org/authors/?q=ai:trancanelli.diegoSummary: Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in \(\mathrm{SU}(2)_k\) quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising (\(k = 2\)), Fibonacci (\(k = 3\)) and Jones-Kauffman (\(k = 4\)) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group in terms of the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.Nonlinearity managed vector solitonshttps://zbmath.org/1541.810352024-09-27T17:47:02.548271Z"Abdullaev, F. Kh."https://zbmath.org/authors/?q=ai:abdullaev.fatkhulla-khabibullaevich|abdullaev.fatkhulla-kh"Yuldashev, J. S."https://zbmath.org/authors/?q=ai:yuldashev.j-s"Ögren, M."https://zbmath.org/authors/?q=ai:ogren.magnusSummary: The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the existence and stability of the vector solitons under the action of the strong nonlinearity management (NM) is investigated. Using a variational approach the parameters of NM vector solitons are found. The numerical simulations of the full time-dependent coupled GPE confirm the theoretical predictions.The first-order factorizable contributions to the three-loop massive operator matrix elements \(A_{Qg}^{(3)}\) and \(\Delta A_{Qg}^{(3)}\)https://zbmath.org/1541.810362024-09-27T17:47:02.548271Z"Ablinger, J."https://zbmath.org/authors/?q=ai:ablinger.jakob"Behring, A."https://zbmath.org/authors/?q=ai:behring.arnd"Blümlein, J."https://zbmath.org/authors/?q=ai:blumlein.johannes"De Freitas, A."https://zbmath.org/authors/?q=ai:de-freitas.abilio"von Manteuffel, A."https://zbmath.org/authors/?q=ai:von-manteuffel.andreas"Schneider, C."https://zbmath.org/authors/?q=ai:schneider.carsten"Schönwald, K."https://zbmath.org/authors/?q=ai:schonwald.kaySummary: The unpolarized and polarized massive operator matrix elements \(A_{Qg}^{(3)}\) and \(\Delta A_{Qg}^{(3)}\) contain first-order factorizable and non-first-order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first-order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color-\(\zeta\) factors for the cases in which also non-first-order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin \(N\)-space, and correspondingly, on Kummer-Poincaré and square-root valued alphabets in Bjorken-\(x\) space. We present a complete discussion of the possibilities of solving the present problem in \(N\)-space analytically and we also discuss the limitations in the present case to analytically continue the given \(N\)-space expressions to \(N\in\mathbb{C}\) by strict methods. The representation through generating functions allows a well synchronized representation of the first-order factorizable results over a 17-letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in \(x\)-space, also containing up to weight \(\mathsf{w = 5}\) special constants, which can be rationalized to Kummer-Poincaré iterated integrals at special arguments. The analytic \(x\)-space representation requires separate analyses for the intervals \(x \in [0, 1/4], [1/4, 1/2], [1/2, 1]\) and \(x > 1\). We also derive the small and large \(x\) limits of the first-order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high-precision numerical solution of the problems.A contribution to the mathematical theory of diffraction: a note on double Fourier integralshttps://zbmath.org/1541.810372024-09-27T17:47:02.548271Z"Assier, R. C."https://zbmath.org/authors/?q=ai:assier.raphael-c"Shanin, A. V."https://zbmath.org/authors/?q=ai:shanin.andrey-v"Korolkov, A. I."https://zbmath.org/authors/?q=ai:korolkov.andrey-iSummary: We consider a large class of physical fields \(u\) written as double inverse Fourier transforms of some functions \(F\) of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to provide a closed-form far-field asymptotic expansion of \(u\). In order to do so, we need to generalise the well-established complex analysis notion of contour indentation to integrals of functions of two complex variables. It is done by introducing the so-called bridge and arrow notation. Thanks to another integration surface deformation, we show that, to achieve our aim, we only need to study a finite number of real points in the Fourier space: the contributing points. This result is called the locality principle. We provide an extensive set of results allowing one to decide whether a point is contributing or not. Moreover, to each contributing point, we associate an explicit closed-form far-field asymptotic component of \(u\). We conclude the article by validating this theory against full numerical computations for two specific examples.On representations of the Helmholtz Green's functionhttps://zbmath.org/1541.810382024-09-27T17:47:02.548271Z"Beylkin, Gregory"https://zbmath.org/authors/?q=ai:beylkin.gregorySummary: We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the oscillatory behavior controlled by the wave number \(k\). The oscillatory component can be chosen to have any finite number of continuous derivatives at the origin and can be applied to a function in the Fourier space in \(\mathcal{O} (k^d \log k)\) operations. The non-oscillatory component has a multiresolution representation via a linear combination of Gaussians and is applied efficiently in space.
Since the Helmholtz Green's function can be viewed as a point source, this partitioning can be interpreted as a splitting into propagating and evanescent components. We show that the non-oscillatory component is significant only in the vicinity of the source at distances \(\mathcal{O} (c_1 k^{- 1} + c_2 k^{- 1} \log_{10} k)\), for some constants \(c_1, c_2\), whereas the propagating component can be observed at large distances.Muon precession from the aspect of Dirac equationshttps://zbmath.org/1541.810392024-09-27T17:47:02.548271Z"He, Jinbo"https://zbmath.org/authors/?q=ai:he.jinbo"Ming, Lei"https://zbmath.org/authors/?q=ai:ming.lei"Tang, Yi-Lei"https://zbmath.org/authors/?q=ai:tang.yilei|tang.yi-lei"Wang, Qiankang"https://zbmath.org/authors/?q=ai:wang.qiankang"Zhang, Hong-Hao"https://zbmath.org/authors/?q=ai:zhang.honghaoSummary: In this paper, we propose a method to compute the muon anomalous precession frequency through solving the wave functions of the Dirac equations straightforwardly. The Lorentz violation terms are also considered. Our method is different from the traditional two-step algorithm in the literature, with the first step to extract the anomalous magnetic momentum factors through the Fouldy-Wouthuysen transformation or Born approximation comparison methods regarding the muon particle as a ``quantum'' object, and the second step to utilize the Thomas-Bargmann-Michel-Telegdi formula regarding the muon particle as a ``classical'' point-like object. Compared with the literature, the method we developed is more consistent and the Lorentz violation terms are taken into account in a unified and straightforward frameset, and expand perturbatively up to the lowest non-trivial order and find out that only \(b_3\), \(c_{11}\), \(c_{22}\), \(H_{12}^\prime\) and \(d_{30}\) affect the precession up to this order.Addition and differentiation of ZX-diagramshttps://zbmath.org/1541.810402024-09-27T17:47:02.548271Z"Jeandel, Emmanuel"https://zbmath.org/authors/?q=ai:jeandel.emmanuel"Perdrix, Simon"https://zbmath.org/authors/?q=ai:perdrix.simon"Veshchezerova, Margarita"https://zbmath.org/authors/?q=ai:veshchezerova.margaritaSummary: The ZX-calculus is a powerful framework for reasoning in quantum computing. It provides in particular a compact representation of matrices of interests. A peculiar property of the ZX-calculus is the absence of a formal sum allowing the linear combinations of arbitrary ZX-diagrams. The universality of the formalism guarantees however that for any two ZX-diagrams, the sum of their interpretations can be represented by a ZX-diagram. We introduce a general, inductive definition of the addition of ZX-diagrams, relying on the construction of controlled diagrams. Based on this addition technique, we provide an inductive differentiation of ZX-diagrams.\par Indeed, given a ZX-diagram with variables in the description of its angles, one can differentiate the diagram according to one of these variables. Differentiation is ubiquitous in quantum mechanics and quantum computing (e.g. for solving optimization problems). Technically, differentiation of ZX-diagrams is strongly related to summation as witnessed by the product rules.\par We also introduce an alternative, non inductive, differentiation technique rather based on the isolation of the variables. Finally, we apply our results to deduce a diagram for an Ising Hamiltonian.
For the entire collection see [Zbl 1491.68017].\(\mathcal{O}(m \alpha^2(Z\alpha)^6)\) contribution to Lamb shift from radiative corrections to the Wichmann-Kroll potentialhttps://zbmath.org/1541.810412024-09-27T17:47:02.548271Z"Krachkov, Petr A."https://zbmath.org/authors/?q=ai:krachkov.petr-a"Lee, Roman N."https://zbmath.org/authors/?q=ai:lee.roman-nSummary: We derive an analytical expression for the contribution of the order \(m\alpha^2(Z\alpha)^6\) to the hydrogen Lamb shift which comes from the diagrams for radiative corrections to the Wichmann-Kroll potential. We use modern methods of multiloop calculations, based on IBP reduction, DRA method and differential equations.Calculation of partition function of Ising model on quantum computerhttps://zbmath.org/1541.810422024-09-27T17:47:02.548271Z"Laba, H. P."https://zbmath.org/authors/?q=ai:laba.h-p"Tkachuk, V. M."https://zbmath.org/authors/?q=ai:tkachuk.volodymyr-mSummary: We study the partition function of the Ising model on a graph with the help of quantum computing. The Boltzmann factor is modeled on a quantum computer as a trace of some evolution operator with effective Hamiltonian over ancilla spins (qubits) corresponding to graph links. We propose two methods for this which are based on effective Hamiltonian with three-spin interaction and on two-spin interaction. The limit of small temperatures allows us to find the ground state of the system that is related to the discrete combinatorial optimization problem. The partition function of the Ising model for two-spin clusters is calculated on IBM's quantum computer. The possibility of finding ground state is also demonstrated for two-spin clusters.Erratum to: ``Triple series evaluated in \(\pi\) and \(\ln 2\) as well as Catalan's constant \(G\)''https://zbmath.org/1541.810432024-09-27T17:47:02.548271Z"Li, Chunli"https://zbmath.org/authors/?q=ai:li.chunli"Chu, Wenchang"https://zbmath.org/authors/?q=ai:chu.wenchangErratum to the authors' paper [ibid. 63, No. 11, 2005--2023 (2023; Zbl 1536.81037)] .Non-symmetric transition probability in generalized qubit modelshttps://zbmath.org/1541.810442024-09-27T17:47:02.548271Z"Niestegge, Gerd"https://zbmath.org/authors/?q=ai:niestegge.gerdSummary: The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their state spaces are strictly convex smooth compact convex sets and that each such set \(K\) gives rise to a quantum logic of this class with the state space \(K\). The transition probabilities are symmetric iff \(K\) is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra.From the binary alphabet to quantum computationhttps://zbmath.org/1541.810452024-09-27T17:47:02.548271Z"Parthasarathy, K. R."https://zbmath.org/authors/?q=ai:parthasarathy.kalyanapuram-rangachariFor the entire collection see [Zbl 1242.00057].Solving large-scale linear systems of equations by a quantum hybrid algorithmhttps://zbmath.org/1541.810462024-09-27T17:47:02.548271Z"Perelshtein, M. R."https://zbmath.org/authors/?q=ai:perelshtein.m-r"Pakhomchik, A. I."https://zbmath.org/authors/?q=ai:pakhomchik.a-i"Melnikov, A. A."https://zbmath.org/authors/?q=ai:melnikov.andrei-andreevich|melnikov.alexey-a"Novikov, A. A."https://zbmath.org/authors/?q=ai:novikov.alexander-a|novikov.andrei-alekseevich"Glatz, A."https://zbmath.org/authors/?q=ai:glatz.andreas"Paraoanu, G. S."https://zbmath.org/authors/?q=ai:paraoanu.gheorghe-sorin"Vinokur, V. M."https://zbmath.org/authors/?q=ai:vinokur.valerii-m"Lesovik, G. B."https://zbmath.org/authors/?q=ai:lesovik.gordey-bSummary: Today's intermediate-scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum-enabled large-scale solutions have been realized only for limited set of problems. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. A classification of linear systems based on the entanglement properties of the associated phase-estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix-to-circuit map. A \(2^{17}\)-dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record-breaking result for a linear system solved by a quantum computer. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution.
{\copyright} 2022 The Authors. Annalen der Physik published by Wiley-VCH GmbHInfluence of the commutator properties of Hamiltonians on the robustness of quantum circuitshttps://zbmath.org/1541.810472024-09-27T17:47:02.548271Z"Slynko, Vitalii"https://zbmath.org/authors/?q=ai:slynko.vitalii-ivanovich"Bivziuk, Vladyslav"https://zbmath.org/authors/?q=ai:bivziuk.vladyslavSummary: We have proved new estimates for the coherent control errors of quantum circuits used in quantum computing. These estimates essentially take into account the commutator properties of the Hamiltonians and are based on the formulas of the commutator calculus.Homological quantum rotor codes: logical qubits from torsionhttps://zbmath.org/1541.810482024-09-27T17:47:02.548271Z"Vuillot, Christophe"https://zbmath.org/authors/?q=ai:vuillot.christophe"Ciani, Alessandro"https://zbmath.org/authors/?q=ai:ciani.alessandro"Terhal, Barbara M."https://zbmath.org/authors/?q=ai:terhal.barbara-mSummary: We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which encode logical oscillators. Unlike for qubits or oscillators, homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code, depending on the homology of the underlying chain complex. In particular, a code based on the chain complex obtained from tessellating the real projective plane or a Möbius strip encodes a qubit. We discuss the distance scalling for such codes which can be more subtle than in the qubit case due to the concept of logical operator spreading by continuous stabilizer phase-shifts. We give constructions of homological quantum rotor codes based on 2D and 3D manifolds as well as products of chain complexes. Superconducting devices being composed of islands with integer Cooper pair charges could form a natural hardware platform for realizing these codes: we show that the \(0 - \pi\) qubit as well as Kitaev's current-mirror qubit -- also known as the Möbius strip qubit -- are indeed small examples of such codes and discuss possible extensions.Distribution of secret keys in a quantum network with trusted intermediate nodeshttps://zbmath.org/1541.810492024-09-27T17:47:02.548271Z"Arbekov, I. M."https://zbmath.org/authors/?q=ai:arbekov.igor-m"Molotkov, S. N."https://zbmath.org/authors/?q=ai:molotkov.sergei-nSummary: The basic configuration in quantum cryptography is a point-to-point configuration. This technology is not applicable to a quantum network, where long-distance distribution of keys is required. In this paper we present a procedure for sequential transfer of an external \(\varepsilon_K\)-secret key through intermediate trusted nodes using \(\varepsilon_i\)-secret keys on separate network segments. It is shown that if the external key is \(\varepsilon_K\)-secret, then after transmission through the trusted node its secrecy becomes equal to \(\varepsilon_K+\varepsilon_1\). The result is generalized to the entire length of the communication line. The secrecy of the transmitted key at the final point becomes \(\varepsilon_L=\varepsilon_K+\sum_{i=1}^L\varepsilon_i\), where \(L\) is the number of this line segments. It is shown that for any measurements of the eavesdropper leading to classical probability distributions the complexity of revealing the transmitted key in the class of algorithms based on the consideration of the most probable keys only are determined by the secrecy parameter \(\varepsilon_L\).An alternative model of quantum key agreement via photon couplinghttps://zbmath.org/1541.810502024-09-27T17:47:02.548271Z"Mu, Yi"https://zbmath.org/authors/?q=ai:mu.yi"Zheng, Yuliang"https://zbmath.org/authors/?q=ai:zheng.yuliangSummary: It has recently been shown that shared cryptographic quantum bits are achievable through the use of an optical coupler, instead of polarised photons. We show that such shared cryptographic bits can also be produced by using a different optical apparatus -- a beam-splitter. An important advantage of such a system is that it could be experimentally more feasible than an optical coupler.
For the entire collection see [Zbl 0855.00046].Asymptotic formula for large eigenvalues of the two-photon quantum Rabi modelhttps://zbmath.org/1541.810512024-09-27T17:47:02.548271Z"Boutet de Monvel, Anne"https://zbmath.org/authors/?q=ai:boutet-de-monvel.anne-marie"Zielinski, Lech"https://zbmath.org/authors/?q=ai:zielinski.lechSummary: We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences \((E_m^+)_{m=0}^\infty\), \((E_m^-)_{m=0}^\infty\) satisfying a three-term asymptotic formula with the remainder estimate \(O(m^{-1}\ln m)\) when \(m\) tends to infinity. By analogy to the one-photon quantum Rabi model, the leading three terms of this asymptotic formula, describe a generalized rotating-wave approximation for large eigenvalues of the two-photon quantum Rabi model.On the origin of black hole paradoxeshttps://zbmath.org/1541.810522024-09-27T17:47:02.548271Z"Hajian, Kamal"https://zbmath.org/authors/?q=ai:hajian.kamalSummary: Black hole firewall paradox is an inconsistency between four postulates in black hole physics: (1) the unitary evolution in quantum systems, (2) application of the semi-classical field theory in low curvature backgrounds, (3) statistical mechanical origin of the black hole entropy, and (4) the equivalence principle in the version of no drama for free-falling observers in the vicinity of the horizon. Based on the existence of the Hawking radiation for the static observers standing outside a Schwarzschild black hole, we show a direct contradiction between the postulates (2) and (4). If there is not a way out of this new problem, it implies the necessity of relaxing one of these two assumptions for resolving the black hole firewall paradox.A fast algorithm for the Schrödinger equation in quaternionic quantum mechanicshttps://zbmath.org/1541.810532024-09-27T17:47:02.548271Z"Jiang, Tongsong"https://zbmath.org/authors/?q=ai:jiang.tongsong"Guo, Zhenwei"https://zbmath.org/authors/?q=ai:guo.zhenwei"Zhang, Dong"https://zbmath.org/authors/?q=ai:zhang.dong"Vasil'ev, V. I."https://zbmath.org/authors/?q=ai:vasilev.vasilii-ivanovichSummary: The eigenvalue problem of a Hermitian quaternion matrix plays a crucial role in quaternion quantum mechanics because it is closely related to the solution of Schrödinger equation. In this paper, a fast algorithm is proposed for finding the eigenvalues and corresponding eigenvectors of a Hermitian quaternion matrix based on the real representation of a quaternion matrix as well as the special structure and properties of a Hermitian quaternion matrix. Numerical experiments demonstrate that, compared with the existing computational methods for the eigenvalue problem of a Hermitian quaternion matrix, the proposed method in this paper not only greatly improves the computational efficiency, but also achieves better experimental results in terms of the corresponding computational errors.Spectral and dynamical contrast on highly correlated Anderson-type modelshttps://zbmath.org/1541.810542024-09-27T17:47:02.548271Z"Matos, Rodrigo"https://zbmath.org/authors/?q=ai:matos.rodrigo"Mavi, Rajinder"https://zbmath.org/authors/?q=ai:mavi.rajinder"Schenker, Jeffrey"https://zbmath.org/authors/?q=ai:schenker.jeffrey-hSummary: We study spectral and dynamical properties of random Schrödinger operators \(H_{\text{Vert}}=-A_{\mathbb{G}_{\text{Vert}}}+V_{\omega }\) and \(H_{\text{Diag}}=-A_{\mathbb{G}_{\text{Diag}}}+V_{\omega }\) on certain two-dimensional graphs \({\mathbb{G}_{\text{Vert}}}\) and \({\mathbb{G}_{\text{Diag}}} \). Differently from the standard Anderson model, the random potentials are not independent but, instead, are constant along any vertical line, i.e \(V_{\omega }(\boldsymbol{n})=\omega (n_1)\), for \(\boldsymbol{n}=(n_1,n_2)\). In particular, the potentials studied here exhibit long range correlations. We present examples where geometric changes to the underlying graph, combined with high disorder, have a significant impact on the spectral and dynamical properties of the operators, leading to contrasting behaviors for the ``diagonal'' and ``vertical'' models. Moreover, the ``vertical'' model exhibits a sharp phase transition within its (purely) absolutely continuous spectrum. This is captured by the notions of transient and recurrent components of the absolutely continuous spectrum, introduced by \textit{J. E. Avron} and \textit{B. Simon} [J. Funct. Anal. 43, 1--31 (1981; Zbl 0488.47021)].Topology of 2D Dirac operators with variable mass and an application to shallow-water waveshttps://zbmath.org/1541.810552024-09-27T17:47:02.548271Z"Rossi, Sylvain"https://zbmath.org/authors/?q=ai:rossi.sylvain"Tarantola, Alessandro"https://zbmath.org/authors/?q=ai:tarantola.alessandroSummary: A Dirac operator on the plane with constant (positive) mass is a Chern insulator, sitting in class D of the Kitaev table. Despite its simplicity, this system is topologically ill-behaved: the non-compact Brillouin zone prevents definition of a bulk invariant, and naively placing the model on a manifold with boundary results in violations of the bulk-edge correspondence (BEC). We overcome both issues by letting the mass spatially vary in the vertical direction, interpolating between the original model and its negative-mass counterpart. Proper bulk and edge indices can now be defined. They are shown to coincide, thereby embodying BEC.
The shallow-water model exhibits the same illnesses as the 2D massive Dirac. Identical problems suggest identical solutions, and indeed extending the approach above to this setting yields proper indices and another instance of BEC.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}Time evolution and the Schrödinger equation on time dependent quantum graphshttps://zbmath.org/1541.810562024-09-27T17:47:02.548271Z"Smilansky, Uzy"https://zbmath.org/authors/?q=ai:smilansky.uzy"Sofer, Gilad"https://zbmath.org/authors/?q=ai:sofer.giladSummary: The purpose of the present paper is to discuss the time dependent Schrödinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show that the well posedness of the Schrödinger equation can be guaranteed by replacing the standard Kirchhoff Laplacian with a magnetic Schrödinger operator with a harmonic potential. We then generalize the result to time dependent families of vertex conditions. We also apply the theory to show the existence of a geometric phase associated with a slowly changing quantum graph.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbativelyhttps://zbmath.org/1541.810572024-09-27T17:47:02.548271Z"Hasler, David"https://zbmath.org/authors/?q=ai:hasler.david-g"Hinrichs, Benjamin"https://zbmath.org/authors/?q=ai:hinrichs.benjamin"Siebert, Oliver"https://zbmath.org/authors/?q=ai:siebert.oliverSummary: The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock representation, one can prove the existence of so-called dressed one-particle states. In this article, we give a simple non-perturbative proof for the existence of such one-particle states at arbitrary coupling strength and for almost all total momenta in a physically motivated momentum region. Our results hold both for the non- and the semi-relativistic Nelson model.On metric controlled operator-valued frames and their applicationshttps://zbmath.org/1541.810582024-09-27T17:47:02.548271Z"Poumai, Khole Timothy"https://zbmath.org/authors/?q=ai:poumai.khole-timothy"Khanna, Nikhil"https://zbmath.org/authors/?q=ai:khanna.nikhil"Kaushik, S. K."https://zbmath.org/authors/?q=ai:kaushik.shiv-kumarSummary: The exploration of pseudo-Hermitian quantum mechanics has led to rapid progress in the methods of constructing inner products and determining the observables of the theory in quantum sciences. In this paper, we introduce metric controlled operator-valued frames and our motivation is to find the applications in the generalized setting of quantum mechanics. We give various characterizations of metric controlled operator-valued frames. We also explore various spectral properties of pseudo-Hermitian and pseudo-unitary operators. Finally, we give the method of representing infinte quantum channels in pseudo-Hermitian quantum mechanics using metric controlled operator-valued frames.
{\copyright 2024 American Institute of Physics}On a limit pass from two-point to one-point interaction in a one dimensional quantum mechanical problem giving rise to a spontaneous symmetry breakinghttps://zbmath.org/1541.810592024-09-27T17:47:02.548271Z"Restuccia, A."https://zbmath.org/authors/?q=ai:restuccia.alvaro"Sotomayor, A."https://zbmath.org/authors/?q=ai:sotomayor.adrian"Shtraus, V. A."https://zbmath.org/authors/?q=ai:strauss.vladimir-abramovichSummary: We analyze, by means of singular potentials defined in terms of Dirac functions and their derivatives, a one dimensional symmetry breaking in quantum mechanics. From a mathematical point of view, we use a technique of selfadjoint extensions applied to a symmetric differential operator with a domain containing smooth functions which vanish at two inner points of the real line. As is well known, the latter leads to a two-point boundary problem. We compute the resolvent of the corresponding extension and investigate its behavior in the case in which the inner points change their positions. The domain of these extensions can contain some functions with non differentiability or discontinuity at the points mentioned before. This fact can be interpreted as a presence of singular potentials like shifted Dirac delta functions and/or their first derivative centered at the same points. Then, we study the existence of broken-symmetry bound states. For some given entanglement boundary conditions we can show the existence of a ground state, which leads to a spontaneous symmetry breaking. We also prove that within a frame of Pontryagin spaces this type of symmetry breaking is saved if the distance between the mentioned above interior points tends to zero and then we can reformulate this result in terms of a larger Hilbert space.Schrödinger operators with dynamically defined potentialshttps://zbmath.org/1541.810602024-09-27T17:47:02.548271Z"Damanik, David"https://zbmath.org/authors/?q=ai:damanik.davidSummary: In this survey, we discuss spectral and quantum dynamical properties of discrete one-dimensional Schrödinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an introductory part explaining basic spectral concepts and fundamental results, we present the general theory of such operators, and then provide an overview of known results for specific classes of potentials. Here we focus primarily on the cases of random and almost periodic potentials.Optimal semiclassical regularity of projection operators and strong Weyl lawhttps://zbmath.org/1541.810612024-09-27T17:47:02.548271Z"Lafleche, Laurent"https://zbmath.org/authors/?q=ai:lafleche.laurentSummary: Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of quantum mechanics, projection operators can be seen as the analogue of characteristic functions of subsets of the phase space, which are discontinuous functions. We prove that projection operators indeed converge to characteristic functions of the phase space and that in terms of quantum Sobolev spaces, they exhibit the same maximal regularity as characteristic functions. This can be interpreted as a semiclassical asymptotic on the size of commutators in Schatten norms. Our study answers a question raised in [\textit{J. J. Chong} et al., J. Eur. Math. Soc. (JEMS), (2024; \url{doi:10.4171/JEMS/1478})] about the possibility of having projection operators as initial data. It also gives a strong convergence result in Sobolev spaces for the Weyl law in phase space.
{\copyright 2024 American Institute of Physics}Semiclassical approximation of functional integrals containing the centrifugal potentialhttps://zbmath.org/1541.810622024-09-27T17:47:02.548271Z"Malyutin, Viktor Borisovich"https://zbmath.org/authors/?q=ai:malyutin.viktor-borisovich"Nurzhanov, Berdakh Orynbaevich"https://zbmath.org/authors/?q=ai:nurzhanov.berdakh-orynbaevichSummary: In this paper, we consider the class of functional integrals with respect to the conditional Wiener measure, which is important for applications. These integrals are written using the action functional containing terms corresponding to kinetic and potential energies. For the considered class of integrals an approach to semiclassical approximation is developed. This approach is based on the decomposition of the action with respect to the classical trajectory. In the expansion of the action, only terms with degrees zero and two are used. A numerical analysis of the accuracy of the semiclassical approximation for functional integrals containing the centrifugal potential is done.Conditions for the existence of eigenvalues of a three-particle lattice model Hamiltonianhttps://zbmath.org/1541.810632024-09-27T17:47:02.548271Z"Bahronov, B. I."https://zbmath.org/authors/?q=ai:bahronov.b-i"Rasulov, T. H."https://zbmath.org/authors/?q=ai:rasulov.tulkin-khusenovich"Rehman, M."https://zbmath.org/authors/?q=ai:rehman.mutti-urSummary: In this article, we present a three-particle lattice model Hamiltonian \({{H}_{{\mu ,\lambda }}}\), \(\mu ,\lambda > 0\) by making use nonlocal potential. The Hamiltonian under consideration acts as a tensor sum of two Friedrichs models \({{h}_{{\mu ,\lambda }}}\) which comprises a rank 2 perturbation associated with a system of three quantum particles on a \(d\)-dimensional lattice. The current study investigates the number of eigenvalues associated with the Hamiltonian. Furthermore, we provide the suitable conditions on the existence of eigenvalues localized inside, in the gap and below the bottom of the essential spectrum of \({{H}_{{\mu ,\lambda }}}\).Generalised graph Laplacians and canonical Feynman integrals with kinematicshttps://zbmath.org/1541.810642024-09-27T17:47:02.548271Z"Brown, Francis"https://zbmath.org/authors/?q=ai:brown.francis-c-sSummary: To any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always finite. They are generalised Feynman integrals which satisfy graphical relations obtained from contracting edges in graphs, and a coproduct involving both ultra-violet and infra-red subgraphs. Their integrands are defined by evaluating bi-invariant forms, which represent stable classes in the cohomology of the general linear group, on a generalised graph Laplacian matrix which depends on the external kinematics of a graph.Gluing Karcher-Scherk saddle towers. I: Triply periodic minimal surfaceshttps://zbmath.org/1541.810652024-09-27T17:47:02.548271Z"Chen, Hao"https://zbmath.org/authors/?q=ai:chen.hao"Traizet, Martin"https://zbmath.org/authors/?q=ai:traizet.martinSummary: We construct minimal surfaces by gluing singly periodic Karcher-Scherk saddle towers along their wings. Such constructions were previously implemented assuming a horizontal reflection plane. We break this symmetry by prescribing phase differences between the saddle towers. It turns out that, in addition to the previously known horizontal balancing condition, the saddle towers must also be balanced under a subtle vertical interaction. This interaction vanishes in the presence of a horizontal reflection plane, hence was not perceived in previous works. Our construction will be presented in a series of papers. In this first paper of the series, we will explain the background of the project and establish the graph theoretical setup that will be useful for all papers in the series. The main task of the current paper is to glue saddle towers into triply periodic minimal surfaces (TPMSs). Our construction expands many previously known TPMSs into new 5-parameter families, therefore significantly advances our knowledge on the space of TPMSs.Surface and guided waves near the interface between the media with an abruptly change in the Dielectric constant and a parabolic permittivity profilehttps://zbmath.org/1541.810662024-09-27T17:47:02.548271Z"Savotchenko, S. E."https://zbmath.org/authors/?q=ai:savotchenko.s-eSummary: The waveguide features of the planar interface separating the different optical media with a parabolic permittivity profile and with an abrupt change in the dielectric constant with growing the electric field are studied. A new form of the dielectric permittivity consisting of a parabolic spatial distribution and an intensity-dependent nonlinear part is proposed. Exact solutions to the wave equation with proposed complicated permittivity describing the new types of surface and guided transverse electric (TE) waves are found in the case of both continuous and discrete spectrum of the effective refractive index. The influence of the optical parameters of the contacting media on the wave distribution profiles and their properties are analyzed. A growing width of graded-index layer makes it possible to enlarge the penetration depth of the surface wave existing in the discrete spectrum and to reduce it in the continuous spectrum.Equations of fluid mechanics with \(\mathcal{N} = 1\) Schrödinger supersymmetryhttps://zbmath.org/1541.810672024-09-27T17:47:02.548271Z"Galajinsky, Anton"https://zbmath.org/authors/?q=ai:galajinsky.anton-vSummary: Equations of fluid mechanics with \(\mathcal{N} = 1\) Schrödinger supersymmetry are formulated within the method of nonlinear realizations of Lie groups.Can the ontology of Bohmian mechanics consists only in particles? The PBR theorem says nohttps://zbmath.org/1541.810682024-09-27T17:47:02.548271Z"Gao, Shan"https://zbmath.org/authors/?q=ai:gao.shanSummary: The meaning of the wave function is an important unresolved issue in Bohmian mechanics. On the one hand, according to the nomological view, the wave function of the universe or the universal wave function is nomological, like a law of nature. On the other hand, the PBR theorem proves that the wave function in quantum mechanics or the effective wave function in Bohmian mechanics is ontic, representing the ontic state of a physical system in the universe. It is usually thought that the nomological view of the universal wave function is compatible with the ontic view of the effective wave function, and thus the PBR theorem has no implications for the nomological view. In this paper, I argue that this is not the case, and these two views are in fact incompatible. This means that if the effective wave function is ontic as the PBR theorem proves, then the universal wave function cannot be nomological, and the ontology of Bohmian mechanics cannot consist only in particles. This incompatibility result holds true not only for Humeanism and dispositionalism but also for primitivism about laws of nature, which attributes a fundamental ontic role to the universal wave function. Moreover, I argue that although the nomological view can be held by rejecting one key assumption of the PBR theorem, the rejection will lead to serious problems, such as that the results of measurements and their probabilities cannot be explained in ontology in Bohmian mechanics. Finally, I briefly discuss three \(\psi\)-ontologies, namely a physical field in a fundamental high-dimensional space, a multi-field in three-dimensional space, and RDMP (Random Discontinuous Motion of Particles) in three-dimensional space, and argue that the RDMP ontology can answer the objections to the \(\psi\)-ontology raised by the proponents of the nomological view.Rotating traversable wormhole geometries in the presence of three-form fieldshttps://zbmath.org/1541.810692024-09-27T17:47:02.548271Z"Tangphati, Takol"https://zbmath.org/authors/?q=ai:tangphati.takol"Chaihao, Butsayapat"https://zbmath.org/authors/?q=ai:chaihao.butsayapat"Samart, Daris"https://zbmath.org/authors/?q=ai:samart.daris"Channuie, Phongpichit"https://zbmath.org/authors/?q=ai:channuie.phongpichit"Momeni, Davood"https://zbmath.org/authors/?q=ai:momeni.davoodSummary: In this work, we study the rotating wormhole geometries supported by a three-form field. We demonstrate for particular choices of parameters that it is possible for the matter fields threading the wormhole to satisfy the null and weak energy conditions throughout the spacetime, when the three-form field is present. In this case, the form field is interpreted as supporting the wormhole and the energy condition violation is restricted only to the 3-form fields. Thus, the three-form curvature terms, which may be interpreted as a gravitational fluid, sustain these wormhole geometries. Additionally, we also address the ergoregion of the solutions.Towards a quadratic Poisson algebra for the subtracted classical monodromy of symmetric space sine-Gordon theorieshttps://zbmath.org/1541.810702024-09-27T17:47:02.548271Z"Delduc, F."https://zbmath.org/authors/?q=ai:delduc.francois"Hoare, B."https://zbmath.org/authors/?q=ai:hoare.ben"Magro, M."https://zbmath.org/authors/?q=ai:magro.marcSummary: Symmetric space sine-Gordon theories are two-dimensional massive integrable field theories, generalising the sine-Gordon and complex sine-Gordon theories. To study their integrability properties on the real line, it is necessary to introduce a subtracted monodromy matrix. Moreover, since the theories are not ultralocal, a regularisation is required to compute the Poisson algebra for the subtracted monodromy. In this article, we regularise and compute this Poisson algebra for certain configurations, and show that it can both satisfy the Jacobi identity and imply the existence of an infinite number of conserved quantities in involution.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd}Bethe ansatz solutions and hidden \(sl(2)\) algebraic structure for a class of quasi-exactly solvable systemshttps://zbmath.org/1541.810712024-09-27T17:47:02.548271Z"Li, Siyu"https://zbmath.org/authors/?q=ai:li.siyu"Marquette, Ian"https://zbmath.org/authors/?q=ai:marquette.ian"Zhang, Yao-Zhong"https://zbmath.org/authors/?q=ai:zhang.yaozhongSummary: The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the singular anharmonic oscillator, the generalized quantum isotonic oscillator, non-polynomially deformed oscillator, and the Schrödinger system from the kink stability analysis of \(\phi^6\)-type field theory. We present a systematic and unified treatment for the odd and even sectors of these models. We find generic closed-form expressions for constraints to the allowed model parameters for quasi-exact solvability, the corresponding energies and wavefunctions. We also make progress in the analysis of solutions to the Bethe ansatz equations in the spaces of model parameters and provide insight into the curves/surfaces of the allowed parameters in the parameter spaces. Most previous analyses in this aspect were on a case-by-case basis and restricted to the first excited states. We present analysis of the solutions (i.e. roots) of the Bethe ansatz equations for higher excited states (up to levels \(n=30\) or 50). The shapes of the root distributions change drastically across different regions of model parameters, illustrating phenomena analogous to phase transition in context of integrable models. Furthermore, we also obtain the \(sl(2)\) algebraization for the class of models in their respective even and odd sectors in a unified way.Metastable oscillations in an evolutionary game: synchronization and controlhttps://zbmath.org/1541.810722024-09-27T17:47:02.548271Z"Vershinina, Olga"https://zbmath.org/authors/?q=ai:vershinina.olga"Ivanchenko, Mikhail"https://zbmath.org/authors/?q=ai:ivanchenko.mikhail-vSummary: Evolutionary games with a finite number of players may manifest transient oscillatory dynamics before reaching an absorbing state. Such oscillations could be prone to synchronization, however its details and specific properties are not known. Here, we investigate synchronization of metastable oscillations in the finite-dimensional evolutionary game ``Battle of the Sexes'', as well as the possibility of controlling the properties of these oscillations by a multiplicative periodic signal. The appropriately generalized frequency and phase quantifiers demonstrate the possibility of synchronization, and the asymmetry of frequency range, induced by the finite size of population. Evolution of oscillations under strengthening periodic driving depends on whether synchronization is reached: in the synchronous regime the amplitude of oscillations grows, while their lifetime decreases, whereas in the asynchronous regime their amplitude decays to zero with the quasi-stationary distribution becoming unimodal.Homotopy of periodic \(2 \times 2\) matriceshttps://zbmath.org/1541.810732024-09-27T17:47:02.548271Z"Avron, Joseph E."https://zbmath.org/authors/?q=ai:avron.joseph-e"Turner, Ari M."https://zbmath.org/authors/?q=ai:turner.ari-mSummary: We describe the homotopy classes of loops in the space of \(2 \times 2\) simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in \(\mathbb{R}^3/\{0\}\). Since closed curves in \(\mathbb{R}^3/\{0\}\) can be readily visualized, no advanced tools of algebraic topology are needed. The matrices represent gapped Bloch Hamiltonians in 1D with a two dimensional Hilbert space per unit cell.
{\copyright 2024 American Institute of Physics}Quantum origin of (Newtonian) mass and Galilean relativity symmetryhttps://zbmath.org/1541.810742024-09-27T17:47:02.548271Z"Kong, Otto C. W."https://zbmath.org/authors/?q=ai:kong.otto-c-wSummary: The Galilei group has been taken as the fundamental symmetry for `nonrelativistic' physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the full picture here, emphasizing aspects that are different from the more familiar picture. The analysis involves a more careful treatment of the relation between the exact mathematics and its physical application in the dynamical theories, and a more serious full implementation of the mathematical logic than what is usually available in the physics literature. The article summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant and the notion of center of mass as dictated by the symmetry, that is particularly also to be seen as the Heisenberg-Weyl symmetry inside it. Another result is the necessary exclusion of the time translational symmetry. The time translational symmetry in the Galilei group plays no role in the formulation of the dynamical theory and does not correspond to the physical time in any nontrivial setting.An algebra of observables for de Sitter spacehttps://zbmath.org/1541.810752024-09-27T17:47:02.548271Z"Chandrasekaran, Venkatesa"https://zbmath.org/authors/?q=ai:chandrasekaran.venkatesa"Longo, Roberto"https://zbmath.org/authors/?q=ai:longo.roberto"Penington, Geoff"https://zbmath.org/authors/?q=ai:penington.geoff"Witten, Edward"https://zbmath.org/authors/?q=ai:witten.edwardSummary: We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type \(\mathrm{II}_1\). There is a natural notion of entropy for a state of such an algebra. There is a maximum entropy state, which corresponds to empty de Sitter space, and the entropy of any semiclassical state of the Type \(\mathrm{II}_1\) algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy \(S_{\mathrm{gen}} = (A/4G_N) + S_{\mathrm{out}}\). An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type \(\mathrm{II}_1\) algebra.Properties of the conformal Yangian in scalar and gauge field theorieshttps://zbmath.org/1541.810762024-09-27T17:47:02.548271Z"Dokmetzoglou, Nikolaos"https://zbmath.org/authors/?q=ai:dokmetzoglou.nikolaos"Dolan, Louise"https://zbmath.org/authors/?q=ai:dolan.louiseSummary: Properties of the \(\mathrm{SO}(2, n)\) Yangian acting on scalar and gauge fields are presented. This differential operator representation of the infinite-dimensional extension of the conformal algebra SO(2\textit{, n}) is proved to satisfy the Serre relation for arbitrary spacetime dimension \(n\) for off-shell scalar theory, but only on shell and for \(n = 4\) in the gauge theory. The \(\mathrm{SO}(2, n)\) Yangian acts simply on the off-shell kinematic invariants \((k_I + k_{I+1} + \dots)^2\), and it annihilates individual off-shell scalar \(\lambda\phi^3\) Feynman tree graphs for \(n = 6\) if the differential operator representation is extended by graph dependent evaluation terms. The \(\mathrm{SO}(2, 4)\) Yangian level one generators are shown to act in a compact way on pure Yang-Mills gluon tree amplitudes. The action of the Yangian on the scattering polynomials of a CHY formalism is also described.Gaudin model for the multinomial distributionhttps://zbmath.org/1541.810772024-09-27T17:47:02.548271Z"Iliev, Plamen"https://zbmath.org/authors/?q=ai:iliev.plamenSummary: The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of polynomials consisting of common eigenfunctions of Gaudin operators in terms of Aomoto-Gelfand hypergeometric series. The construction shows that the polynomials in this basis are also common eigenfunctions of the operators for a dual Gaudin model acting on the degree indices, and therefore, they provide a solution to a multivariate discrete bispectral problem.Point particle \(\mathcal{E}\)-modelshttps://zbmath.org/1541.810782024-09-27T17:47:02.548271Z"Klimčík, Ctirad"https://zbmath.org/authors/?q=ai:klimcik.ctiradSummary: We show that the same algebraic data that permit to construct the Lax pair and the \(r\)-matrix of an integrable non-linear \(\sigma\)-model in 1 + 1 dimensions can be also used for the construction of Lax pairs and of \(r\)-matrices of several other non-trivial integrable theories in 1 + 0 dimension. We call those new integrable theories the point particle \(\mathcal{E}\)-models, we describe their structure and give their physical interpretation. We work out in detail the point particle \(\mathcal{E}\)-models associated to the bi-Yang-Baxter deformation of the \(SU(N)\) principal chiral model. In particular, for each complex flag manifold we thus obtain a two-parameter family of integrable models living on it.
{\copyright 2024 American Institute of Physics}On Derkachov-Manashov \(R\)-matrices for the principal series of unitary representationshttps://zbmath.org/1541.810792024-09-27T17:47:02.548271Z"Neretin, Yury A."https://zbmath.org/authors/?q=ai:neretin.yuri-aSummary: In 2001--2013 textit{S. È. Derkachëv} and \textit{A. N. Manashov} [Nucl. Phys., B 617, No. 1--3, 375--440 (2001; Zbl 0976.82011); St. Petersbg. Math. J. 21, No. 4, 513--577 (2010; Zbl 1194.81123); translation from Algebra Anal. 21, No. 4, 1--94 (2009); SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 084, 20 p. (2006; Zbl 1138.82009)] with coauthors obtained simple and natural expressions of \(R\)-matrices for the principal series of representations of the groups \(\mathrm{SL}(2,\mathbb{C})\), \(\mathrm{SL}(2,\mathbb{R})\), \(\mathrm{SL}(n,\mathbb{C})\), \(\mathrm{SO}(1, n)\). The Yang-Baxter identities for these intertwining operators are kinds of multivariate hypergeometric transformations. Derivations of the identities are based on calculations ``of physical level of rigor'' with divergent integrals. Our purpose is a formal mathematical justification of these results.
{\copyright 2024 American Institute of Physics}Lagrangian reduction by stages in field theoryhttps://zbmath.org/1541.810802024-09-27T17:47:02.548271Z"Berbel, Miguel Á."https://zbmath.org/authors/?q=ai:berbel.miguel-angel"Castrillón López, Marco"https://zbmath.org/authors/?q=ai:castrillon-lopez.marcoSummary: We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange-Poincaré bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame.Covariant quantum combinatorics with applications to zero-error communicationhttps://zbmath.org/1541.810812024-09-27T17:47:02.548271Z"Verdon, Dominic"https://zbmath.org/authors/?q=ai:verdon.dominicSummary: We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite-dimensional \(C^*\)-algebras) carry an action of a compact quantum group \(G\), and all channels (completely positive maps preserving a certain \(G\)- invariant functional) are covariant with respect to the \(G\)-actions. We motivate our definitions by applications to zero-error quantum communication theory with a symmetry constraint. Some key results are the following: (1) We give a necessary and sufficient condition for a covariant quantum relation to be the underlying relation of a covariant channel. (2) We show that every quantum confusability graph with a \(G\)-action (which we call a quantum \(G\)-graph) arises as the confusability graph of a covariant channel. (3) We show that a covariant channel is reversible precisely when its confusability \(G\)-graph is discrete. (4) When \(G\) is quasitriangular (this includes all compact groups), we show that covariant zero-error source-channel coding schemes are classified by covariant homomorphisms between confusability \(G\)-graph.On the set of reduced states of translation invariant, infinite quantum systemshttps://zbmath.org/1541.810822024-09-27T17:47:02.548271Z"Blakaj, Vjosa"https://zbmath.org/authors/?q=ai:blakaj.vjosa"Wolf, Michael M."https://zbmath.org/authors/?q=ai:wolf.michael-marc|mclean-wolf.michaelSummary: The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of algebraic approximations that become tight only in the limit of infinitely many auxiliary variables. We show that this is necessarily so for any algebraic ansatz by proving that the set of reduced states is not semialgebraic. We also provide evidence that additional elementary transcendental functions cannot lead to a finitary description.Dirac electron free field anticommutator and its zeros on time intervalshttps://zbmath.org/1541.810832024-09-27T17:47:02.548271Z"Karatsuba, E. A."https://zbmath.org/authors/?q=ai:karatsuba.ekatherina-aSummary: Estimates are obtained for time intervals containing a zero of the Pauli-Jordan-Dirac anticommutator in a discrete representation in the one- and three-dimensional cases.Ladder operators with no vacuum, their coherent states, and an application to graphenehttps://zbmath.org/1541.810842024-09-27T17:47:02.548271Z"Bagarello, F."https://zbmath.org/authors/?q=ai:bagarello.fabioSummary: In literature ladder operators of different nature exist. The most famous are those obeying canonical (anti-) commutation relations, but they are not the only ones. In our knowledge, all ladder operators have a common feature: the lowering operators annihilate a non zero vector, the \textit{vacuum}. This is connected to the fact that operators of these kind are often used in factorizing some positive operators, or some operators which are bounded from below. This is the case, of course, of the harmonic oscillator, but not only. In this paper we discuss what happens when considering lowering operators with no vacua. In particular, after a general analysis of this situation, we propose a possible construction of coherent states, and we apply our construction to graphene.Borel summability of the \(1/N\) expansion in quartic \(\mathrm{O}(N)\)-vector modelshttps://zbmath.org/1541.810852024-09-27T17:47:02.548271Z"Ferdinand, L."https://zbmath.org/authors/?q=ai:ferdinand.leonard"Gurau, R."https://zbmath.org/authors/?q=ai:gurau.razvan-g"Perez-Sanchez, C. I."https://zbmath.org/authors/?q=ai:perez-sanchez.carlos-ignacio"Vignes-Tourneret, F."https://zbmath.org/authors/?q=ai:vignes-tourneret.fabienSummary: We consider a quartic \(\mathrm{O}(N)\)-vector model. Using the loop vertex expansion, we prove the Borel summability in \(1/N\) along the real axis of the partition function and of the connected correlations of the model. The Borel summability holds uniformly in the coupling constant, as long as the latter belongs to a cardioid like domain of the complex plane, avoiding the negative real axis.QDT -- a Matlab toolbox for the simulation of coupled quantum systems and coherent multidimensional spectroscopyhttps://zbmath.org/1541.810862024-09-27T17:47:02.548271Z"Kenneweg, Tristan"https://zbmath.org/authors/?q=ai:kenneweg.tristan"Mueller, Stefan"https://zbmath.org/authors/?q=ai:muller.stefan.10|muller.stefan.2|muller.stefan.3|muller.stefan.5|mueller.stefan|muller.stefan.8|muller.stefan.4|muller.stefan.9|muller.stefan.6|muller.stefan.7|muller.stefan-c|muller-arisona.stefan|muller.stefan.1"Brixner, Tobias"https://zbmath.org/authors/?q=ai:brixner.tobias"Pfeiffer, Walter"https://zbmath.org/authors/?q=ai:pfeiffer.walterSummary: We present QDT (``quantum dynamics toolbox''), an open-source Matlab software package that enables users to simulate coupled quantum systems in the subsystem energy eigenbasis using modular functions. QDT requires no user knowledge of operator matrix assembly and automatically performs all necessary operator constructions and Hilbert space expansions. Density matrix propagation is performed by numerically solving the Liouville-von-Neumann equation. In order to simulate dissipation and decoherence effects, the Lindblad formalism is implemented. Furthermore, QDT supplies practical analysis and plotting functions, such as visualization of density matrix and expectation value dynamics, that facilitate the evaluation of simulation results. QDT further provides a module for the simulation of coherent multidimensional spectroscopy.Tuning the separability in noncommutative spacehttps://zbmath.org/1541.810872024-09-27T17:47:02.548271Z"Patra, Pinaki"https://zbmath.org/authors/?q=ai:patra.pinaki.1Summary: With the help of the generalized Peres-Horodecki separability criterion (Simon's condition) for a bipartite Gaussian state, we have studied the separability of the noncommutative (NC) space coordinate degrees of freedom. Non-symplectic nature of the transformation between the usual commutative space and NC space restricts the straightforward use of Simon's condition in NCS. We have transformed the NCS system to an equivalent Hamiltonian in commutative space through the Bopp shift, which enables the utilization of the separability criterion. To make our study fairly general and to analyze the effect of parameters on the separability of bipartite state in NC-space, we have considered a bilinear Hamiltonian with time-dependent (TD) parameters, along with a TD external interaction, which is linear in field modes. The system is transformed (\(\mathrm{Sp}(4, \mathbb{R})\)) into canonical form keeping the intrinsic symplectic structure intact. The solution of the TD-Schrödinger equation is obtained with the help of the Lewis-Riesenfeld invariant method (LRIM). Expectation values of the observables (thus the covariance matrix) are constructed from the states obtained from LRIM. It turns out that the existence of the NC parameters in the oscillator determines the separability of the states. In particular, for isotropic oscillators, the separability condition for the bipartite Gaussian states depends on specific values of NC parameters. Moreover, particular anisotropic parameter values for the oscillator may cease the separability. In other words, both the deformation parameters \((\theta, \eta)\) and parameter values of the oscillator (mass, frequency) are important characteristics for the separability of bipartite Gaussian states. Thus tuning the parameter values, one can destroy or recreate the separability of states. With the help of a toy model, we have demonstrated how the tuning of a TD-NC space parameter affects the separability.
{\copyright 2024 American Institute of Physics}A local trace formula for \(p\)-adic infinitesimal symmetric spaces: the case of Guo-Jacquethttps://zbmath.org/1541.810882024-09-27T17:47:02.548271Z"Li, Huajie"https://zbmath.org/authors/?q=ai:li.huajieSummary: We establish an invariant local trace formula for the tangent space of some symmetric spaces over a non-archimedean local field of characteristic zero. These symmetric spaces are studied in Guo-Jacquet trace formulae, and our methods are inspired by works of Waldspurger and Arthur. Some other results are given during the proof including a noninvariant local trace formula, Howe's finiteness for weighted orbital integrals, and the representability of the Fourier transform of weighted orbital integrals. These local results are preparations for the comparison of regular semi-simple terms, which are weighted orbital integrals, appearing in an infinitesimal variant of Guo-Jacquet trace formulae.The ABCD of topological recursionhttps://zbmath.org/1541.810892024-09-27T17:47:02.548271Z"Andersen, Jørgen Ellegaard"https://zbmath.org/authors/?q=ai:andersen.jorgen-ellegaard"Borot, Gaëtan"https://zbmath.org/authors/?q=ai:borot.gaetan"Chekhov, Leonid O."https://zbmath.org/authors/?q=ai:chekhov.leonid-o"Orantin, Nicolas"https://zbmath.org/authors/?q=ai:orantin.nicolasSummary: Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of \([43]\), seeing it as a quantisation of certain quadratic Lagrangians in \(T^\ast V\) for some vector space \(V\). KS topological recursion is a procedure which takes as initial data a quantum Airy structure -- a family of at most quadratic differential operators on \(V\) satisfying some axioms -- and gives as outcome a formal series of functions on \(V\) (the partition function) simultaneously annihilated by these operators. Finding and classifying quantum Airy structures modulo the gauge group action, is by itself an interesting problem which we study here. We provide some elementary, Lie-algebraic tools to address this problem, and give some elements of the classification for \(\dim V = 2\). We also describe four more interesting classes of quantum Airy structures, coming from respectively Frobenius algebras (here we retrieve the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a \(\mathbb{Z}_2\)-invariant version of the latter. This \(\mathbb{Z}_2\)-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of \([43]\).Trace distance ergodicity for quantum Markov semigroupshttps://zbmath.org/1541.810902024-09-27T17:47:02.548271Z"Bertini, Lorenzo"https://zbmath.org/authors/?q=ai:bertini.lorenzo-bertini"De Sole, Alberto"https://zbmath.org/authors/?q=ai:de-sole.alberto"Posta, Gustavo"https://zbmath.org/authors/?q=ai:posta.gustavoSummary: We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this criterion to the bosonic and fermionic Ornstein-Uhlenbeck semigroups and to a family of quantum Markov semigroups parametrized by semisimple Lie algebras and their irreducible representations, in which the Lindblad generator is given by the adjoint action of the Casimir element.On the relation between quantum Darwinism and approximate quantum Markovianityhttps://zbmath.org/1541.810912024-09-27T17:47:02.548271Z"Guo, Xiao-Kan"https://zbmath.org/authors/?q=ai:guo.xiao-kan"Huang, Zhiqiang"https://zbmath.org/authors/?q=ai:huang.zhiqiangSummary: There are strong evidences in the literature that quantum non-Markovianity would hinder the presence of Quantum Darwinism. In this Letter, we study the relation between quantum Darwinism and approximate quantum Markovianity for open quantum systems by exploiting the properties of quantum conditional mutual information. We show that for approximately Markovian quantum processes the conditional mutual information still has the scaling property for Quantum Darwinism. Then two general bounds on the backflow of information are obtained, with which we can show that the presence of Quantum Darwinism restricts the information backflow and the quantum non-Markovianity must be small.A new characterization of homogeneous functions and applicationshttps://zbmath.org/1541.810922024-09-27T17:47:02.548271Z"Elghribi, Moncef"https://zbmath.org/authors/?q=ai:elghribi.moncefSummary: We present a new characterization of real homogeneous functions of a negative degree by a new counterpart of Euler's homogeneous function theorem using quantum calculus and replacing the classical derivative operator by a \((p, q)\)-derivative operator. As an application we study the solution of the Cauchy problem associated to the \((p, q)\)-analogue of the Euler operator. Using this solution, a probabilistic interpretation is given in some details; more specifically, we prove that this solution is a stochastically continuous Markovian transition operator. Finally, we study its associated subordinated stochastically Markovian transition operator.Area law for steady states of detailed-balance local Lindbladianshttps://zbmath.org/1541.810932024-09-27T17:47:02.548271Z"Firanko, Raz"https://zbmath.org/authors/?q=ai:firanko.raz"Goldstein, Moshe"https://zbmath.org/authors/?q=ai:goldstein.moshe"Arad, Itai"https://zbmath.org/authors/?q=ai:arad.itaiSummary: We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state \(\sigma\). We show that under mild assumptions on the Lindbladian terms, which can be checked efficiently, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum and a ground state that is the vectorization of \(\sigma^{1/2}\). Consequently, we can use Hamiltonian complexity tools to study the steady states of such open systems. In particular, we show an area-law in the mutual information for the steady state of such 1D systems, together with a tensor-network representation that can be found efficiently.
{\copyright 2024 American Institute of Physics}On the path integral formulation of Wigner-Dunkl quantum mechanicshttps://zbmath.org/1541.810942024-09-27T17:47:02.548271Z"Junker, Georg"https://zbmath.org/authors/?q=ai:junker.georgSummary: Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which exhibits the same dispersion relation as observed in standard quantum mechanics. Feynman's path integral approach is then extended to Wigner-Dunkl quantum mechanics. The harmonic oscillator problem is solved explicitly. We then look at the Euclidean time evolution and the related Dunkl process. This process, which exhibit jumps, can be represented by two continuous Bessel processes, one with reflection and one with absorption at the origin. The Feynman-Kac path integral for the harmonic oscillator problem is explicitly calculated.
{{\copyright} 2024 IOP Publishing Ltd}Topological strings on non-commutative resolutionshttps://zbmath.org/1541.810952024-09-27T17:47:02.548271Z"Katz, Sheldon"https://zbmath.org/authors/?q=ai:katz.sheldon"Klemm, Albrecht"https://zbmath.org/authors/?q=ai:klemm.albrecht"Schimannek, Thorsten"https://zbmath.org/authors/?q=ai:schimannek.thorsten"Sharpe, Eric"https://zbmath.org/authors/?q=ai:sharpe.eric-rSummary: In this paper we propose a definition of torsion refined Gopakumar-Vafa (GV) invariants for Calabi-Yau threefolds with terminal nodal singularities that do not admit Kähler crepant resolutions. Physically, the refinement takes into account the charge of five-dimensional BPS states under a discrete gauge symmetry in M-theory. We propose a mathematical definition of the invariants in terms of the geometry of all non-Kähler crepant resolutions taken together. The invariants are encoded in the A-model topological string partition functions associated to non-commutative (nc) resolutions of the Calabi-Yau. Our main example will be a singular degeneration of the generic Calabi-Yau double cover of \({\mathbb{P}}^3\) and leads to an enumerative interpretation of the topological string partition function of a hybrid Landau-Ginzburg model. Our results generalize a recent physical proposal made in the context of torus fibered Calabi-Yau manifolds by one of the authors and clarify the associated enumerative geometry.\texttt{FeynMG}: a \texttt{FeynRules} extension for scalar-tensor theories of gravityhttps://zbmath.org/1541.810962024-09-27T17:47:02.548271Z"Sevillano Muñoz, Sergio"https://zbmath.org/authors/?q=ai:munoz.sergio-sevillano"Copeland, Edmund J."https://zbmath.org/authors/?q=ai:copeland.edmund-j"Millington, Peter"https://zbmath.org/authors/?q=ai:millington.peter"Spannowsky, Michael"https://zbmath.org/authors/?q=ai:spannowsky.michaelSummary: The ability to represent perturbative expansions of interacting quantum field theories in terms of simple diagrammatic rules has revolutionized calculations in particle physics (and elsewhere). Moreover, these rules are readily automated, a process that has catalyzed the rise of symbolic algebra packages. However, in the case of extended theories of gravity, such as scalar-tensor theories, it is necessary to precondition the Lagrangian to apply this automation or, at the very least, to take advantage of existing software pipelines. We present a \texttt{Mathematica} code \texttt{FeynMG}, which works in conjunction with the well-known package \texttt{FeynRules}, to do just that: \texttt{FeynMG} takes as inputs the \texttt{FeynRules} model file for a non-gravitational theory and a user-supplied gravitational Lagrangian. \texttt{FeynMG} provides functionality that inserts the minimal gravitational couplings of the degrees of freedom specified in the model file, determines the couplings of the additional tensor and scalar degrees of freedom (the metric and the scalar field from the gravitational sector), and preconditions the resulting Lagrangian so that it can be passed to \texttt{FeynRules}, either directly or by outputting an updated \texttt{FeynRules} model file. The Feynman rules can then be determined and output through \texttt{FeynRules}, using existing universal output formats and interfaces to other analysis packages.Exact renormalization groups and transportation of measureshttps://zbmath.org/1541.810972024-09-27T17:47:02.548271Z"Shenfeld, Yair"https://zbmath.org/authors/?q=ai:shenfeld.yairSummary: This note provides a new perspective on Polchinski's exact renormalization group, by explaining how it gives rise, via the multiscale Bakry-Émery criterion, to Lipschitz transport maps between Gaussian free fields and interacting quantum and statistical field theories. Consequently, many functional inequalities can be verified for the latter field theories, going beyond the current known results.Unfolded Fierz-Pauli equations in three-dimensional asymptotically flat spacetimeshttps://zbmath.org/1541.810982024-09-27T17:47:02.548271Z"Ammon, Martin"https://zbmath.org/authors/?q=ai:ammon.martin"Pannier, Michel"https://zbmath.org/authors/?q=ai:pannier.michelSummary: We utilise a quotient of the universal enveloping algebra of the Poincaré algebra in three spacetime dimensions, on which we formulate a covariant constancy condition. The equations so obtained contain the Fierz-Pauli equations for non-interacting, massive higher-spin fields, and can thus be regarded as an unfolding of the Fierz-Pauli system. All fundamental fields completely decouple from each other. In the non-truncated case, the field content includes infinitely many copies of each field at fixed spin.Late-time correlation functions in \(\mathrm{dS}_3/\mathrm{CFT}_2\) correspondencehttps://zbmath.org/1541.810992024-09-27T17:47:02.548271Z"Chen, Heng-Yu"https://zbmath.org/authors/?q=ai:chen.heng-yu"Chen, Shi"https://zbmath.org/authors/?q=ai:chen.shi"Hikida, Yasuaki"https://zbmath.org/authors/?q=ai:hikida.yasuakiSummary: We compute the late-time correlation functions on three-dimensional de Sitter spacetime for a higher-spin gravity theory. For this, we elaborate on the formulation to obtain the wave functional of universe from a dual conformal field theory, which is used to compute the late-time correlation functions. We argue that the relation to direct bulk Feynman diagram computations in the in-in formulation. We furthermore provide a precise prescription to construct a higher-spin \(\mathrm{dS}_3\) holography as an analytic continuation of Gaberdiel-Gopakumar duality for \(\mathrm{AdS}_3\). Part of results here were already reported in an earlier letter. We explain the details of their derivations and extend the analysis to more generic cases in this paper. Previously, we have examined two- and three-point functions and a simple four-point correlator at the leading order in Newton constant. Here we also evaluate more complicated four-point correlators. Finally, we study late-time correlators in an alternative limit of \(\mathrm{dS}_3/\mathrm{CFT}_2\) with critical level coset, such as, two-point correlator on conical defect geometry. We also examine one-loop corrections to two-point correlator on \(\mathrm{dS}_3\).Constraining higher-spin \(S\)-matriceshttps://zbmath.org/1541.811002024-09-27T17:47:02.548271Z"Tran, Tung"https://zbmath.org/authors/?q=ai:tran.tungSummary: There are various no-go theorems that tightly constrain the existence of local higher-spin theories with non-trivial \(S\)-matrix in flat space. Due to the existence of higher-spin Yang-Mills theory with non-trivial scattering amplitudes, it makes sense to revisit Weinberg's soft theorem -- a direct consequence of the Lorentz invariance of the \(S\)-matrix that does not take advantage of unitarity and parity invariance. By working with the chiral representation -- a representation originated from twistor theory, we show that Weinberg's soft theorem can be evaded and non-trivial higher-spin \(S\)-matrix is possible. In particular, we show that Weinberg's soft theorem is more closely related to the number of derivatives in the interactions rather than spins. We also observe that all constraints imposed by gauge invariance of the \(S\)-matrix are accompanied by polynomials in the soft momentum of the emitted particle where the zeroth order in the soft momentum is a charge conservation law.Parity violation in the scalar trispectrum: no-go theorems and yes-go exampleshttps://zbmath.org/1541.811012024-09-27T17:47:02.548271Z"Cabass, Giovanni"https://zbmath.org/authors/?q=ai:cabass.giovanni"Jazayeri, Sadra"https://zbmath.org/authors/?q=ai:jazayeri.sadra"Pajer, Enrico"https://zbmath.org/authors/?q=ai:pajer.enrico"Stefanyszyn, David"https://zbmath.org/authors/?q=ai:stefanyszyn.davidSummary: We derive a set of no-go theorems and yes-go examples for the parity-odd primordial trispectrum of curvature perturbations. We work at tree-level in the decoupling limit of the Effective Field Theory of Inflation and assume scale invariance and a Bunch-Davies vacuum. We show that the parity-odd scalar trispectrum vanishes in the presence of any number of scalar fields with arbitrary mass and any parity-odd scalar correlator vanishes in the presence of any number of spinning fields with massless de Sitter mode functions, in agreement with the findings of \textit{T. Liu} at al. [J. High Energy Phys. 2020, No. 4, Paper No. 189, 37 p. (2020; \url{doi:10.1007/JHEP04(2020)189})]. The same is true for correlators with an odd number of conformally-coupled external fields. We derive these results using both the (boostless) cosmological bootstrap, in particular the Cosmological Optical Theorem, and explicit perturbative calculations. We then discuss a series of yes-go examples by relaxing the above assumptions one at the time. In particular, we provide explicit results for the parity-odd trispectrum for (i) violations of scale invariance in single-clock inflation, (ii) the modified dispersion relation of the ghost condensate (non-Bunch-Davies vacuum), and (iii) interactions with massive spinning fields. Our results establish the parity-odd trispectrum as an exceptionally sensitive probe of new physics beyond vanilla inflation.Evanescent operators in one-loop matching computationshttps://zbmath.org/1541.811022024-09-27T17:47:02.548271Z"Fuentes-Martín, Javier"https://zbmath.org/authors/?q=ai:fuentes-martin.javier"König, Matthias"https://zbmath.org/authors/?q=ai:konig.matthias"Pagès, Julie"https://zbmath.org/authors/?q=ai:pages.julie"Thomsen, Anders Eller"https://zbmath.org/authors/?q=ai:thomsen.anders-eller"Wilsch, Felix"https://zbmath.org/authors/?q=ai:wilsch.felixSummary: Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces -- the evanescent operators -- can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.Amplitude's positivity vs. subluminality: causality and unitarity constraints on dimension 6 \& 8 gluonic operators in the SMEFThttps://zbmath.org/1541.811032024-09-27T17:47:02.548271Z"Ghosh, Diptimoy"https://zbmath.org/authors/?q=ai:ghosh.diptimoy"Sharma, Rajat"https://zbmath.org/authors/?q=ai:sharma.rajat"Ullah, Farman"https://zbmath.org/authors/?q=ai:ullah.farmanSummary: We derive the causality and unitarity constraints on dimension 6 and dimension 8 Gluon field strength operators in the Standard Model Effective Field Theory (SMEFT). In the first part of the paper, we use the `amplitude analysis' i.e. dispersion relation for \(2 \rightarrow 2\) scattering in the forward limit, to put bounds on the Wilson coefficients. We show that the dimension 6 operators can exist only in the presence of certain dimension 8 operators. It is interesting that the square of the dimension 6 Wilson coefficients can be constrained in this case even at the tree level. In the second part of this work, we successfully rederive all these bounds using the classical causality argument that demands that the speed of fluctuations about any non-trivial background should not exceed the speed of light. We also point out some subtleties in the superluminality analysis regarding whether the low-frequency phase velocity can always be used as the relevant quantity for Causality violation: as an example, we show that, due to these subtleties, if a small pion mass is added in the chiral Lagrangian, it is unclear if any strict positivity bound can be derived on the dimension 8 Wilson coefficient. Finally, we mention an interesting non-relativistic example where the subluminality requirement produces a stronger bound than the `amplitude analysis'.Hilbert series, the Higgs mechanism, and HEFThttps://zbmath.org/1541.811042024-09-27T17:47:02.548271Z"Gráf, Lukáš"https://zbmath.org/authors/?q=ai:graf.lukas"Henning, Brian"https://zbmath.org/authors/?q=ai:henning.brian"Lu, Xiaochuan"https://zbmath.org/authors/?q=ai:lu.xiaochuan"Melia, Tom"https://zbmath.org/authors/?q=ai:melia.tom"Murayama, Hitoshi"https://zbmath.org/authors/?q=ai:murayama.hitoshiSummary: We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest at the level of the Hilbert series, as expected for the partition function of an \(S\)-matrix that is subject to the Goldstone equivalence theorem. In addition to massive vectors, we detail how other massive, spinning particles can be studied with Hilbert series; in particular, we spell out the ingredients for massive gravity in general spacetime dimensions. Further methodology is introduced to enable Hilbert series to capture the effect of spurion fields acquiring vevs. We apply the techniques to the Higgs Effective Field Theory (HEFT), providing a systematic enumeration of its operator basis. This is achieved both from a direct and a custodial symmetry spurion-based approach; we compare and contrast the two approaches, and our results to those appearing in previous literature.Renormalization of the standard model effective field theory from geometryhttps://zbmath.org/1541.811052024-09-27T17:47:02.548271Z"Helset, Andreas"https://zbmath.org/authors/?q=ai:helset.andreas"Jenkins, Elizabeth E."https://zbmath.org/authors/?q=ai:jenkins.elizabeth-e"Manohar, Aneesh V."https://zbmath.org/authors/?q=ai:manohar.aneesh-vSummary: \(S\)-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature \(R_{ijkl}\) of this combined space, with indices \(i\), \(j\), \(k\), \(l\) chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight.Gravity as a gapless phase and biform symmetrieshttps://zbmath.org/1541.811062024-09-27T17:47:02.548271Z"Hinterbichler, Kurt"https://zbmath.org/authors/?q=ai:hinterbichler.kurt"Hofman, Diego M."https://zbmath.org/authors/?q=ai:hofman.diego-m"Joyce, Austin"https://zbmath.org/authors/?q=ai:joyce.austin"Mathys, Grégoire"https://zbmath.org/authors/?q=ai:mathys.gregoireSummary: We study effective field theories (EFTs) enjoying (maximal) biform symmetries. These are defined by the presence of a conserved (electric) current that has the symmetries of a Young tableau with two columns of equal length. When these theories also have a topological (magnetic) biform current, its conservation law is anomalous. We go on to show that this mixed anomaly uniquely fixes the two-point function between the electric and magnetic currents. We then perform a Källén-Lehmann spectral decomposition of the current-current correlator, proving that there is a massless mode in the spectrum, whose masslessness is protected by the anomaly. Furthermore, the anomaly gives rise to a universal form of the EFT whose most relevant term -- which resembles the linear Einstein action -- dominates the infrared physics. As applications of this general formalism, we study the theories of a Galileon superfluid and linearized gravity. Thus, one can view the masslessness of the graviton as being protected by the anomalous biform symmetries. The associated EFT provides an organizing principle for gravity at low energies in terms of physical symmetries, and allows interactions consistent with linearized diffeomorphism invariance. These theories are not ultraviolet-complete -- the relevant symmetries can be viewed as emergent -- nor do they include the nonlinearities necessary to make them fully diffeomorphism invariant, so there is no contradiction with the expectation that quantum gravity cannot have any global symmetries.Soft theorems for boosts and other time symmetrieshttps://zbmath.org/1541.811072024-09-27T17:47:02.548271Z"Hui, Lam"https://zbmath.org/authors/?q=ai:hui.lam"Joyce, Austin"https://zbmath.org/authors/?q=ai:joyce.austin"Komissarov, Ilia"https://zbmath.org/authors/?q=ai:komissarov.ilia"Parmentier, Klaas"https://zbmath.org/authors/?q=ai:parmentier.klaas"Santoni, Luca"https://zbmath.org/authors/?q=ai:santoni.luca"Wong, Sam S. C."https://zbmath.org/authors/?q=ai:wong.sam-s-cSummary: We derive soft theorems for theories in which time symmetries -- symmetries that involve the transformation of time, an example of which are Lorentz boosts -- are spontaneously broken. The soft theorems involve unequal-time correlation functions with the insertion of a soft Goldstone in the far past. Explicit checks are provided for several examples, including the effective theory of a relativistic superfluid and the effective field theory of inflation. We discuss how in certain cases these unequal-time identities capture information at the level of observables that cannot be seen purely in terms of equal-time correlators of the field alone. We also discuss when it is possible to phrase these soft theorems as identities involving equal-time correlators.Gluonic evanescent operators: two-loop anomalous dimensionshttps://zbmath.org/1541.811082024-09-27T17:47:02.548271Z"Jin, Qingjun"https://zbmath.org/authors/?q=ai:jin.qingjun"Ren, Ke"https://zbmath.org/authors/?q=ai:ren.ke"Yang, Gang"https://zbmath.org/authors/?q=ai:yang.gang.3"Yu, Rui"https://zbmath.org/authors/?q=ai:yu.ruiSummary: Evanescent operators are a special class of operators that vanish in four-dimensional spacetime but are non-zero in \(d = 4 - 2\epsilon\) dimensions. In this paper, we continue our systematic study of the evanescent operators in the pure Yang-Mills theory and focus on their two-loop renormalization. We develop an efficient strategy to compute the two-loop divergences of form factors of high-dimensional and high-length operators by combining the \(d\)-dimensional unitarity method and the improved tensor reduction techniques. Two-loop anomalous dimensions are obtained for the dimension-10 basis in the planar YM theory, for which both the \(\overline{\mathrm{MS}}\) scheme and the finite-renormalization scheme are used. We verify that the two-loop anomalous dimensions are the same in these two schemes at the Wilson-Fisher conformal fixed point. Our computation shows that the evanescent operators are indispensable in order to obtain the correct two-loop anomalous dimensions. This work provides a first computation of the two-loop anomalous dimensions of the complete set of dimension-10 operators. The method we use is also expected to provide an efficient strategy for the two-loop renormalization of general high-dimensional operators.Tangleoids with quantum field theories in biosystemshttps://zbmath.org/1541.811092024-09-27T17:47:02.548271Z"Ozel, Cenap"https://zbmath.org/authors/?q=ai:ozel.cenap"Albeladi, Hadeel"https://zbmath.org/authors/?q=ai:albeladi.hadeel"Linker, Patrick"https://zbmath.org/authors/?q=ai:linker.patrickSummary: The open question whether quantum field theories can be used in biological systems will be addressed in this study. Quantum effects were reported for certain biological systems like the magnetic orientation sense in migratory birds. In quantum field theories it is possible to derive effective quantum field theories with welded tangleoids including braid relations that describe composite particles based on the dynamics of microscopic particle where these composite particles are made of. We observe that the generators of the tangleoid category that will depict the Feynman graphs are \(X\) for a scattering vertex. This arises after carrying out the integral over bosonic fields \(A_\mu\) in the partition function (D) that will lead to an four-valent interaction vertex generated by a quartic term in the fermionic fields. With \(X_+\) and \(X_-\) we will depict order changes like that regarding time orderings. Ordinary propagators are depicted by \(\cup\) and \(\cap\). Finally, the generators ! and \(\text{{!`}}\) come into play if other foreign fields are picked up.Twistors, the ASD Yang-Mills equations and 4d Chern-Simons theoryhttps://zbmath.org/1541.811102024-09-27T17:47:02.548271Z"Bittleston, Roland"https://zbmath.org/authors/?q=ai:bittleston.roland"Skinner, David"https://zbmath.org/authors/?q=ai:skinner.davidSummary: We show that the approaches to integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations are closely related, at least classically. Following a suggestion of Kevin Costello, we start from holomorphic Chern-Simons theory on twistor space, defined with the help of a meromorphic \((3, 0)\)-form \(\Omega \). If \(\Omega\) is nowhere vanishing, it descends to a theory on 4d space-time with classical equations of motion equivalent to the anti-self-dual Yang-Mills equations. Examples include a 4d analogue of the Wess-Zumino-Witten model and a theory of a Lie algebra valued scalar with a cubic two derivative interaction. Under symmetry reduction, these yield actions for 2d integrable systems. On the other hand, performing the symmetry reduction directly on twistor space reduces holomorphic Chern-Simons theory to the 4d Chern-Simons theory with disorder defects studied by \textit{K. Costello} and \textit{M. Yamazaki} [``Gauge theory and integrability, III'', Preprint, \url{arXiv:1908.02289}]. Finally we show that a similar reduction by a single translation leads to a 5d partially holomorphic Chern-Simons theory describing the Bogomolny equations.New relations for tree-level form factors and scattering amplitudeshttps://zbmath.org/1541.811112024-09-27T17:47:02.548271Z"Dong, Jin"https://zbmath.org/authors/?q=ai:dong.jin"He, Song"https://zbmath.org/authors/?q=ai:he.song"Lin, Guanda"https://zbmath.org/authors/?q=ai:lin.guandaSummary: We show that tree-level form factors with length-two operators in Yang-Mills-scalar (YMS) theory exhibit structures very similar to scattering amplitudes of gluons and scalars, which leads to new relations between them. Just like amplitudes, \(n\)-point Yang-Mills form factors with \(\operatorname{tr}(F^2)\) operator can be decomposed as a linear combination of form factors with \(\operatorname{tr}(\phi^2)\) operator and \(r\) external scalars in YMS theory, where the coefficients are given by Lorentz products of the \(r\) linearized field strengths. Moreover, we show that any such \(n\)-point form factor of \(\operatorname{tr}(\phi^2)\) operator can be further expanded into \((n+1)\)-point YMS amplitudes with an additional off-shell scalar leg. In addition to unravelling hidden structures, our results provide an efficient algorithm for computing all-multiplicity length-two form factors in any dimension, as well as their Cachazo-He-Yuan formulae via those of the YMS amplitudes.The variational problem and background field in the renormalization group method for nonlinear sigma modelshttps://zbmath.org/1541.811122024-09-27T17:47:02.548271Z"Goswami, Abhishek"https://zbmath.org/authors/?q=ai:goswami.abhishekSummary: We study the variational problem as described by Balaban in his renormalization group method for Yang-Mills theories in \(d = 3, 4\) and adapt it to a class of nonlinear sigma models in \(d=2\). The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis.Quantum field theory with ghost pairshttps://zbmath.org/1541.811132024-09-27T17:47:02.548271Z"Liu, Jiangfan"https://zbmath.org/authors/?q=ai:liu.jiangfan"Modesto, Leonardo"https://zbmath.org/authors/?q=ai:modesto.leonardo"Calcagni, Gianluca"https://zbmath.org/authors/?q=ai:calcagni.gianlucaSummary: We explicitly show that general local higher-derivative theories with \textit{only} complex conjugate ghosts and normal real particles are unitary at any perturbative order in the loop expansion. The proof presented here relies on integrating the loop energies on complex paths resulting from the deformation of the purely imaginary paths, when the external energies are continued from imaginary to real values. Contrary to the case of nonlocal theories, where the same integration path was first proposed, for the classes of theories studied here the same procedure is not analytic, but the resulting theory is unitary and unique when the complex ghosts are present in pairs. As an explicit application, a special class of higher-derivative super-renormalizable or finite gravitational and gauge theories turns out to be unitary at any perturbative order if we exclude the complex ghosts from the spectrum of the theory, as it is normally accepted for Becchi-Rouet-Stora-Tyutin (BRST) ghosts. Finally, we propose an analogy between confined gluons in quantum Yang-Mills theory and classical complex pairs in local higher-derivative theories. According to such interpretation, complex ghosts will not appear on shell as asymptotic states because confined in what is natural to name ``ghostballs.''Radiative phase space extensions at all orders in \(r\) for self-dual Yang-Mills and gravityhttps://zbmath.org/1541.811142024-09-27T17:47:02.548271Z"Nagy, Silvia"https://zbmath.org/authors/?q=ai:nagy.silvia"Peraza, Javier"https://zbmath.org/authors/?q=ai:peraza.javierSummary: Working in the self-dual sector for Yang-Mills and gravity, we show how to construct an extended phase space at null infinity, to all orders in the radial expansion. This formalises the symmetry origin of the infrared behaviour of these theories to all subleading orders. As a corollary, we also derive a double copy mapping from a subset of YM gauge transformations to a subset of diffeomorphisms to all orders in the transformation parameters, which to our knowledge has not been presented before in the literature.Gauge theory geography: charting a path between semiclassical islandshttps://zbmath.org/1541.811152024-09-27T17:47:02.548271Z"Poppitz, Erich"https://zbmath.org/authors/?q=ai:poppitz.erich"Wandler, F. David"https://zbmath.org/authors/?q=ai:wandler.f-davidSummary: We study two semiclassical limits of SU(2) Yang-Mills theory on a spatial torus with a 't Hooft twist: the ``femtouniverse,'' where all \(\mathbb{T}^3\) directions are small, and deformed Yang-Mills theory on \(\mathbb{T}^2\times\mathbb{S}^1\), with small \(\mathbb{S}^1\) and large or infinite \(\mathbb{T}^2\). Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch \(\theta\)-dependent vacuum structure of these theories. We then calculate the one-loop potential for the \(\mathbb{S}^1\)-holonomy in the presence of twists on \(\mathbb{T}^2\). We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial \(\mathbb{T}^2\times\mathbb{S}^1\), with a twist in the \(\mathbb{T}^2\). The results point towards some interesting features worthy of further study.Deciphering colour building blocks of massive multiparton amplitudes at 4-loops and beyondhttps://zbmath.org/1541.811162024-09-27T17:47:02.548271Z"Agarwal, Neelima"https://zbmath.org/authors/?q=ai:agarwal.neelima"Pal, Sourav"https://zbmath.org/authors/?q=ai:pal.sourav|pal.sourav.1"Srivastav, Aditya"https://zbmath.org/authors/?q=ai:srivastav.aditya"Tripathi, Anurag"https://zbmath.org/authors/?q=ai:tripathi.anurag.1Summary: The soft function in non-abelian gauge theories exponentiate, and their logarithms can be organised in terms of the collections of Feynman diagrams called Cwebs. The colour factors that appear in the logarithm are controlled by the web mixing matrices. Direct construction of the diagonal blocks of Cwebs using the new concepts of Normal ordering, basis Cweb and Fused-Web was recently carried out in [\textit{N. Agarwal} et al., J. High Energy Phys. 2022, No. 6, Paper No. 20, 60 p. (2022; Zbl 1522.81242)]. In this article we establish correspondence between the boomerang webs introduced in [\textit{E. Gardi} et al., J. High Energy Phys. 2021, No. 12, Paper No. 18, 86 p. (2021; Zbl 1521.81444)] and non-boomerang Cwebs. We use this correspondence together with Uniqueness theorem and Fused web formalism introduced in [Agarwal et al., loc. cit.] to obtain the diagonal blocks of four general classes of Cwebs to all orders in perturbation theory which also cover all the four loop Boomerang Cwebs connecting four Wilson lines. We also fully construct the mixing matrix of a special Cweb to all orders in perturbation theory.Loop corrections in Minkowski spacetime away from equilibrium. I: Late-time resummationshttps://zbmath.org/1541.811172024-09-27T17:47:02.548271Z"Chaykov, Spasen"https://zbmath.org/authors/?q=ai:chaykov.spasen"Agarwal, Nishant"https://zbmath.org/authors/?q=ai:agarwal.nishant"Bahrami, Sina"https://zbmath.org/authors/?q=ai:bahrami.sina"Holman, R."https://zbmath.org/authors/?q=ai:holman.richard|holman.r-aSummary: Loop corrections to unequal-time correlation functions in Minkowski spacetime exhibit secular growth due to a breakdown of time-dependent perturbation theory. This is analogous to secular growth in equal-time correlators on time-dependent backgrounds, except that in Minkowski the divergences must not signal a real IR issue. In this paper, we calculate the late-time limit of the two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background. We first use a late-time version of the in-in path integral starting in the vacuum of the free theory; in this limit, the calculation, including UV renormalization, reduces to that in in-out. We find linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. We next develop the Weisskopf-Wigner resummation method, that proceeds by demanding unitarity within a truncated Hilbert space, to calculate the resummed correlator and find that it gives an exact exponentiation of the late-time perturbative result. The resummed (unequal-time) correlator thus decays with an exponential or polynomial time-dependence, which is suggestive of `universal' behavior that depends on the dimensions of the interaction strength.Loop corrections in Minkowski spacetime away from equilibrium. II: Finite-time resultshttps://zbmath.org/1541.811182024-09-27T17:47:02.548271Z"Chaykov, Spasen"https://zbmath.org/authors/?q=ai:chaykov.spasen"Agarwal, Nishant"https://zbmath.org/authors/?q=ai:agarwal.nishant"Bahrami, Sina"https://zbmath.org/authors/?q=ai:bahrami.sina"Holman, R."https://zbmath.org/authors/?q=ai:holman.richard|holman.r-aSummary: Loop corrections to finite-time correlation functions in quantum field theories away from equilibrium can be calculated using the in-in path integral approach. In this paper, we calculate the unequal-time two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background, starting the field evolution at an arbitrary initial time. We find the counterterms that need to be added to UV-renormalize the result, including usual in-out counterterms in the dynamics and additional initial state counterterms that are required to cancel all UV divergences. We find that the late-time limit of the renormalized correlation function exhibits a linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. The late-time correlations match those obtained in our companion paper and, as shown there, the divergences do not indicate a real IR issue, consistent with what one would expect in Minkowski.
For Part I, see [\textit{S. Chaykov} et al., J. High Energy Phys. 2023, No. 2, Paper No. 93, 29 p. (2023; Zbl 1541.81117)].Four-loop HQET propagators from the DRA methodhttps://zbmath.org/1541.811192024-09-27T17:47:02.548271Z"Lee, Roman N."https://zbmath.org/authors/?q=ai:lee.roman-n"Pikelner, Andrey F."https://zbmath.org/authors/?q=ai:pikelner.andrey-fSummary: We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared to previous applications of the DRA method, we apply a new technique of fixing homogeneous solutions from pole parts of integrals evaluated in different rational space-time dimension points. The latter were calculated from the integration-by-parts reduction of finite integrals in shifted space-time dimension and/or with increased propagators powers. We provide results for epsilon expansions of master integrals near \(d = 4\) and \(d = 3\) using constructed alternative sets of integrals with expansion coefficients having conjectural uniform transcendental weight.Towards the non-perturbative cosmological bootstraphttps://zbmath.org/1541.811202024-09-27T17:47:02.548271Z"Hogervorst, Matthijs"https://zbmath.org/authors/?q=ai:hogervorst.matthijs"Penedones, Joao"https://zbmath.org/authors/?q=ai:penedones.joao"Vaziri, Kamran Salehi"https://zbmath.org/authors/?q=ai:vaziri.kamran-salehiSummary: We study quantum field theory on a de Sitter spacetime \(\mathrm{dS}_{d+1}\) background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group \(\mathrm{SO}(d + 1, 1)\). As the first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of the scalar bulk two-point function. In the process, we exhibit a relation between poles in the corresponding spectral densities and the boundary CFT data. Moreover, we derive an inversion formula for the spectral density through analytical continuation from the sphere and use it to find the spectral decompisiton for a few examples. Next, we study the conformal partial wave decomposition of the four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity properties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in \(\mathrm{dS}_2\).QFT approach to dressed particle processes in preheating and non-perturbative mechanism in kinematically-forbidden regimehttps://zbmath.org/1541.811212024-09-27T17:47:02.548271Z"Taya, Hidetoshi"https://zbmath.org/authors/?q=ai:taya.hidetoshi"Yamada, Yusuke"https://zbmath.org/authors/?q=ai:yamada.yusukeSummary: We provide a quantum-field theoretic formulation of dressed particle dynamics that systematically includes particle production and scattering/decay processes in the preheating era. Our approach is based on the so-called perturbation theory in the Furry picture, in which coherent background fields (i.e., inflaton and the expanding Universe) are treated non-perturbatively whereas interactions between dressed particles are taken into account perturbatively. As an application, we consider the instant preheating mechanism and compute the number of produced particles explicitly. We find a novel non-perturbative particle-production mechanism, which is kinematically forbidden within the conventional perturbative calculation and gives the dominant contribution in certain parameter regimes, e.g., light daughter particles.Bulk gauge fields and holographic RG from exact RGhttps://zbmath.org/1541.811222024-09-27T17:47:02.548271Z"Dharanipragada, Pavan"https://zbmath.org/authors/?q=ai:dharanipragada.pavan"Dutta, Semanti"https://zbmath.org/authors/?q=ai:dutta.semanti"Sathiapalan, B."https://zbmath.org/authors/?q=ai:sathiapalan.balaSummary: Recently, a method was described for deriving Holographic RG equation in \(AdS_{D+1}\) space starting from an Exact RG equation of a \(D\)-dimensional boundary CFT [\textit{B. Sathiapalan} and \textit{H. Sonoda}, Nucl. Phys., B 924, 603--642 (2017; Zbl 1373.81292)]. The evolution operator corresponding to the Exact RG equation was rewritten as a functional integral of a \(D + 1\) dimensional field theory in \(AdS_{D+1}\) space. This method has since been applied to elementary scalars and composite scalars in the \(O(N)\) model [\textit{B. Sathiapalan}, Nucl. Phys., B 959, Article ID 115142, 44 p. (2020; Zbl 1473.81126)]. In this paper, we apply this technique to the conserved vector current and the energy momentum tensor of a boundary CFT, the \(O(N)\) model at a fixed point. These composite spin one and spin two operators are represented by auxiliary fields and extend into the bulk as gauge fields and metric perturbations. We obtain, at the free level, the (gauge fixed) Maxwell and Einstein actions. While the steps involved are motivated by the AdS/CFT correspondence, none of the steps logically require the AdS/CFT conjecture for their justification.Module intersection and uniform formula for iterative reduction of one-loop integralshttps://zbmath.org/1541.811232024-09-27T17:47:02.548271Z"Chen, Jiaqi"https://zbmath.org/authors/?q=ai:chen.jiaqi"Feng, Bo"https://zbmath.org/authors/?q=ai:feng.boSummary: In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants.Holographic Lieb lattice and gapping its Dirac bandhttps://zbmath.org/1541.811242024-09-27T17:47:02.548271Z"Han, Young-Kwon"https://zbmath.org/authors/?q=ai:han.young-kwon"Seo, Jeong-Won"https://zbmath.org/authors/?q=ai:seo.jeong-won"Yuk, Taewon"https://zbmath.org/authors/?q=ai:yuk.taewon"Sin, Sang-Jin"https://zbmath.org/authors/?q=ai:sin.sang-jinSummary: We first point out that the Laia-Tong model realizes the Lieb lattice in the holographic setup. It generates a flat band of sharp particle spectrum together with a Dirac band of unparticle spectrum. We provided an understanding why the Laia-Tong model's boundary condition generate a flat band and compared it with the mechanism of ``compact localized orbits'' in the lattice models to provide a physical reason why Lieb and Laia-Tong model should be identified based on the similarity in the flat band generation mechanism. We then construct a model which opens a gap to the Dirac band so that one can realize a well-separated flat band. We then study the phase transition between the gapped and gapless phases analytically. We also made methodological progress to find a few other possible quantizations and we express the Green functions in any quantization in terms of that in the standard quantization. Finally we carried out the problem of back reaction to show that the qualitative feature remains the same.Three-particle Lellouch-Lüscher formalism in moving frameshttps://zbmath.org/1541.811252024-09-27T17:47:02.548271Z"Müller, Fabian"https://zbmath.org/authors/?q=ai:muller.fabian.1|muller.fabian-l"Pang, Jin-Yi"https://zbmath.org/authors/?q=ai:pang.jin-yi"Rusetsky, Akaki"https://zbmath.org/authors/?q=ai:rusetsky.akaki"Wu, Jia-Jun"https://zbmath.org/authors/?q=ai:wu.jiajunSummary: A manifestly relativistic-invariant Lellouch-Lüscher formalism for the decays into three identical particles with no two-to-three transitions is proposed. Similarly to [\textit{F. Müller} and \textit{A. Rusetsky}, J. High Energy Phys. 2021, No. 3, Paper No. 152, 16 p. (2021; \url{doi:10.1007/JHEP03(2021)152})], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in [\textit{F. Müller} et al., J. High Energy Phys. 2022, No. 2, Paper No. 158, 37 p. (2022; Zbl 1522.81295)], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.Gluon transverse-momentum-dependent distributions from large-momentum effective theoryhttps://zbmath.org/1541.811262024-09-27T17:47:02.548271Z"Zhu, Ruilin"https://zbmath.org/authors/?q=ai:zhu.ruilin"Ji, Yao"https://zbmath.org/authors/?q=ai:ji.yao"Zhang, Jian-Hui"https://zbmath.org/authors/?q=ai:zhang.jianhui"Zhao, Shuai"https://zbmath.org/authors/?q=ai:zhao.shuaiSummary: We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the \(\overline{\mathrm{MS}}\) scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for the extraction of gluon TMDPDFs from lattice simulations, and have the potential to greatly facilitate perturbative calculations of the hard matching kernel.Thermal correlators and bosonization dualities in large \(N\) Chern-Simons matter theorieshttps://zbmath.org/1541.811272024-09-27T17:47:02.548271Z"Ghosh, Sudip"https://zbmath.org/authors/?q=ai:ghosh.sudip"Mazumdar, Subhajit"https://zbmath.org/authors/?q=ai:mazumdar.subhajitSummary: We consider 3-dimensional conformal field theories with \(\mathrm{U}(N)_\kappa\) Chern-Simons gauge fields coupled to bosonic and fermionic matter fields transforming in the fundamental representation of the gauge group. In these CFTs, we compute in the 't Hooft large \(N\) limit and to all orders in the 't Hooft coupling \(\lambda = N/\kappa\), the thermal two-point correlation functions of the spin \(s = 0\), \(s = 1\) and \(s = 2\) gauge invariant conformal primary operators. These are the lowest dimension single trace scalar, the U(1) current and the stress tensor operators respectively. Our results furnish additional tests of the conjectured bosonization dualities in these theories at finite temperature.\(D = 5\) holomorphic Chern-Simons and the pure spinor superstringhttps://zbmath.org/1541.811282024-09-27T17:47:02.548271Z"Berkovits, Nathan"https://zbmath.org/authors/?q=ai:berkovits.nathan-jSummary: The physical states of \(D = 5\) holomorphic Chern-Simons theory correspond to on-shell \(D =10\) open superstring states in the cohomology of \(q_+\), where \(q_+\) is one of the 16 spacetime supersymmetry generators. Scattering amplitudes of these states can be computed either using the usual Ramond-Neveu-Schwarz (RNS) superstring prescription with \(N = 1\) worldsheet supersymmetry, or using a topological \(\hat{c} = 5\) string theory with twisted \(N = 2\) worldsheet supersymmetry.
It will be argued that the relation between \(D = 5\) holomophic Chern-Simons and the RNS superstring is identical to the relation between the pure spinor superstring and the recently constructed B-RNS-GSS superstring which has both \(N = 1\) worldsheet supersymmetry and \(D = 10\) spacetime supersymmetry. Physical states of the pure spinor superstring correspond to on-shell B-RNS-GSS states which are in the cohomology of \(\lambda^\alpha q_\alpha\), where \(\lambda^\alpha\) is a \(D = 10\) pure spinor. And scattering amplitudes of these states can be computed either using the full B-RNS-GSS superstring prescription with \(N = 1\) worldsheet supersymmetry, or using the pure spinor superstring amplitude prescription with twisted \(N = 2\) worldsheet supersymmetry. This should be useful for proving equivalence of the RNS and pure spinor amplitude prescriptions and for clarifying the relation of their multiloop subtleties.A proof for string three-point functions in \(\mathrm{AdS}_3\)https://zbmath.org/1541.811292024-09-27T17:47:02.548271Z"Bufalini, Davide"https://zbmath.org/authors/?q=ai:bufalini.davide"Iguri, Sergio"https://zbmath.org/authors/?q=ai:iguri.sergio-manuel"Kovensky, Nicolas"https://zbmath.org/authors/?q=ai:kovensky.nicolasSummary: Correlation functions of the \(\mathrm{SL}(2, \mathbb{R})\)-WZW model involving spectrally flowed vertex operators are notoriously difficult to compute. An explicit integral expression for the corresponding three-point functions was recently conjectured in [\textit{A. Dei} and \textit{L. Eberhardt}, J. High Energy Phys. 2021, No. 8, Paper No. 25, 48 p. (2021; Zbl 1469.83037)]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [\textit{S. Iguri} and \textit{N. Kovensky}, SciPost Phys. 13, Paper No. 115, 14 p. (2022; \url{doi:10.21468/SciPostPhys.13.5.115})] based on the so-called \(\mathrm{SL}(2, \mathbb{R})\) series identifications, which relate vertex operators belonging to different spectral flow sectors. We also highlight the role of holomorphic covering maps in this context. Our results constitute an important milestone for proving this instance of the \(\mathrm{AdS}_3/\mathrm{CFT}_2\) holographic duality at finite 't Hooft coupling.Normalization of D instanton amplitudes in two dimensional type 0B string theoryhttps://zbmath.org/1541.811302024-09-27T17:47:02.548271Z"Chakravarty, Joydeep"https://zbmath.org/authors/?q=ai:chakravarty.joydeep"Sen, Ashoke"https://zbmath.org/authors/?q=ai:sen.ashokeSummary: We compute the normalization of the D-instanton amplitudes in type 0B string theory in two dimensions and find perfect agreement with the dual matrix model result.Line defects in three dimensional mirror symmetry beyond ADE quivershttps://zbmath.org/1541.811312024-09-27T17:47:02.548271Z"Dey, Anindya"https://zbmath.org/authors/?q=ai:dey.anindyaSummary: Understanding the map of line defects in a Quantum Field Theory under a given duality is generically a difficult problem. This paper is the second in a series which aims to address this question in the context of 3d \(\mathcal{N} = 4\) mirror symmetry. A general prescription for constructing vortex defects and their mirror maps in quiver gauge theories beyond the \(A\)-type was presented by the author in an earlier paper [J. High Energy Phys. 2022, No. 7, Paper No. 114, 101 p. (2022; Zbl 1522.81343)], where specific examples involving \(D\)-type and affine \(D\)-type quivers were discussed. In this paper, we apply the aforementioned prescription to construct a family of vortex defects as coupled 3d-1d systems in quiver gauge theories beyond the \textit{ADE}-type, and study their mirror maps. Specifically, we focus on a class of quiver gauge theories involving unitary gauge nodes with edge multiplicity greater than 1, i.e. two gauge nodes in these theories may be connected by multiple bifundamental hypermultiplets. Quiver gauge theories of this type arise as 3d mirrors of certain Argyres-Douglas theories compactified on a circle. Some of these quiver gauge theories are known to have a pair of 3d mirrors, which are themselves related by an IR duality, discussed recently in [\textit{A. Dey}, ``Higgs branches of Argyres-Douglas theories as quiver varieties'', Preprint, \url{arXiv:2109.07493}]. For a concrete example where a pair of 3d mirrors do exist, we study how the vortex defects constructed using our prescription map to Wilson defects in each mirror theory.Unifying the 6D \(\mathcal{N} = (1, 1)\) string landscapehttps://zbmath.org/1541.811322024-09-27T17:47:02.548271Z"Fraiman, Bernardo"https://zbmath.org/authors/?q=ai:fraiman.bernardo"De Freitas, Héctor Parra"https://zbmath.org/authors/?q=ai:de-freitas.hector-parraSummary: We propose an organizing principle for string theory moduli spaces in six dimensions with \(\mathcal{N} = (1, 1)\), based on a rank reduction map, into which all known constructions fit. In the case of cyclic orbifolds, which are the main focus of the paper, we make an explicit connection with meromorphic 2D (s)CFTs with \(c = 24\) (\(c = 12\)) and show how these encode every possible gauge symmetry enhancement in their associated 6D theories. These results generalize naturally to non-cyclic orbifolds, into which the only known string construction (to our awareness) also fits. This framework suggests the existence of a total of 47 moduli spaces: the Narain moduli space, 23 of cyclic orbifold type and 23 of non-cyclic type. Of these only 17 have known string constructions. Among the 30 new moduli spaces, 15 correspond to pure supergravity, for a total of 16 such spaces. A full classification of nonabelian gauge symmetries is given, and as a byproduct we complete the one for seven dimensions, in which only those of theories with heterotic descriptions were known exhaustively.Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseuxhttps://zbmath.org/1541.811332024-09-27T17:47:02.548271Z"Grozdanov, Sašo"https://zbmath.org/authors/?q=ai:grozdanov.saso"Lemut, Timotej"https://zbmath.org/authors/?q=ai:lemut.timotejSummary: Assuming only a known dispersion relation of a single mode in the spectrum of a meromorphic two-point function (in the complex frequency plane at fixed wavevector) in some quantum field theory, we investigate when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, we develop a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. For concreteness, we focus on theories in which the known mode is a gapless excitation described by the hydrodynamic gradient expansion, known at least to some (preferably high) order. We first apply the algorithm to a simple algebraic example and then to the transverse momentum excitations in the holographic theory that describes a stack of M2 branes and includes momentum diffusion as its gapless excitation.Erratum to: ``Holographic M5 branes in \(AdS_7 \times S^4\)''https://zbmath.org/1541.811342024-09-27T17:47:02.548271Z"Gupta, Varun"https://zbmath.org/authors/?q=ai:gupta.varun.2|gupta.varun.1|gupta.varunErratum to the author's paper [ibid. 2021, No. 12, Paper No. 32, 17 p. (2021; Zbl 1521.81226)].Nonrelativistic approximations of closed bosonic string theoryhttps://zbmath.org/1541.811352024-09-27T17:47:02.548271Z"Hartong, Jelle"https://zbmath.org/authors/?q=ai:hartong.jelle"Have, Emil"https://zbmath.org/authors/?q=ai:have.emilSummary: We further develop the string \(1/c^2\) expansion of closed bosonic string theory, where \(c\) is the speed of light. The expansion will be performed up to and including the next-to-next-to-leading order (NNLO). We show that the next-to-leading order (NLO) theory is equal to the Gomis-Ooguri string, generalised to a curved target space, provided the target space geometry admits a certain class of co-dimension-2 foliations. We compute the energy of the string up to NNLO for a flat target space with a circle that must be wound by the string, and we show that it agrees with the \(1/c^2\) expansion of the relativistic energy. We also compute the algebra of Noether charges for a flat target space and show that this matches order-by-order with an appropriate expansion of the Poincaré algebra, which at NLO gives the string Bargmann algebra. Finally, we expand the phase space action, which allows us to perform the Dirac procedure and pass to the quantum theory. It turns out that the Poisson brackets change at each order, and we show that the normal ordering constant of the relativistic theory, which does not depend on \(c\), can be reproduced by the NLO and NNLO theories.Large U(1) charges from flux breaking in 4D F-theory modelshttps://zbmath.org/1541.811362024-09-27T17:47:02.548271Z"Li, Shing Yan"https://zbmath.org/authors/?q=ai:li.shing-yan"Taylor, Washington"https://zbmath.org/authors/?q=ai:taylor.washington-ivSummary: We study the massless charged spectrum of U(1) gauge fields in F-theory that arise from flux breaking of a nonabelian group. The U(1) charges that arise in this way can be very large. In particular, using vertical flux breaking, we construct an explicit 4D F-theory model with a U(1) decoupled from other gauge sectors, in which the massless/light fields have charges as large as 657. This result greatly exceeds prior results in the literature. We argue heuristically that this result may provide an upper bound on charges for light fields under decoupled U(1) factors in the F-theory landscape. We also show that the charges can be even larger when the U(1) is coupled to other gauge groups.Symmetries of Calabi-Yau prepotentials with isomorphic flopshttps://zbmath.org/1541.811372024-09-27T17:47:02.548271Z"Lukas, Andre"https://zbmath.org/authors/?q=ai:lukas.andre"Ruehle, Fabian"https://zbmath.org/authors/?q=ai:ruehle.fabianSummary: Calabi-Yau threefolds with infinitely many flops to isomorphic manifolds have an extended Kähler cone made up from an infinite number of individual Kähler cones. These cones are related by reflection symmetries across flop walls. We study the implications of this cone structure for mirror symmetry, by considering the instanton part of the prepotential in Calabi-Yau threefolds. We show that such isomorphic flops across facets of the Kähler cone boundary give rise to symmetry groups isomorphic to Coxeter groups. In the dual Mori cone, non-flopping curve classes that are identified under these groups have the same Gopakumar-Vafa invariants. This leads to instanton prepotentials invariant under Coxeter groups, which we make manifest by introducing appropriate invariant functions. For some cases, these functions can be expressed in terms of theta functions whose appearance can be linked to an elliptic fibration structure of the Calabi-Yau manifold.EFT strings and emergencehttps://zbmath.org/1541.811382024-09-27T17:47:02.548271Z"Marchesano, Fernando"https://zbmath.org/authors/?q=ai:marchesano.fernando"Melotti, Luca"https://zbmath.org/authors/?q=ai:melotti.lucaSummary: We revisit the Emergence Proposal in 4d \(\mathcal{N} = 2\) vector multiplet sectors that arise from type II string Calabi-Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA compactifications, where EFT strings arise from NS5-branes wrapping internal four-cycles, and consider a set of infinite-distance moduli-space limits that can be classified in terms of a scaling weight \(w = 1, 2, 3\). It has been shown before how one-loop threshold effects of an infinite tower of BPS particles made up of D2/D0-branes generate the asymptotic behaviour of the gauge kinetic functions along limits with \(w = 3\). We extend this result to \(w = 2\) limits, by taking into account D2-brane multi-wrapping numbers. In \(w = 1\) limits the leading tower involves EFT string oscillations, and one can reproduce the behaviour of both weakly and strongly-coupled U(1)'s independently on whether the EFT string is critical or not, by assuming that charged modes dominate the light spectrum.Row-column duality and combinatorial topological stringshttps://zbmath.org/1541.811392024-09-27T17:47:02.548271Z"Padellaro, Adrian"https://zbmath.org/authors/?q=ai:padellaro.adrian"Radhakrishnan, Rajath"https://zbmath.org/authors/?q=ai:radhakrishnan.rajath"Ramgoolam, Sanjaye"https://zbmath.org/authors/?q=ai:ramgoolam.sanjayeSummary: Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological string theories (CTST). These CTST were based on Dijkgraaf-Witten theories of flat \(G\)-bundles for finite groups \(G\) in two dimensions, denoted \(G\)-TQFTs. We define analogous combinatorial topological strings related to two dimensional topological field theories (TQFTs) based on fusion coefficients of finite groups. These TQFTs are denoted as \(R(G)\)-TQFTs and allow analogous integrality results to be derived for partial row sums of characters over conjugacy classes along fixed rows. This relation between the \(G\)-TQFTs and \(R(G)\)-TQFTs defines a row-column duality for character tables, which provides a physical framework for exploring the mathematical analogies between rows and columns of character tables. These constructive proofs of integrality are complemented with the proof of similar and complementary results using the more traditional Galois theoretic framework for integrality properties of character tables. The partial row and column sums are used to define generalised partitions of the integer row and column sums, which are of interest in combinatorial representation theory.
{{\copyright} 2024 IOP Publishing Ltd}Mass spectrum of type IIB flux compactifications -- comments on AdS vacua and conformal dimensionshttps://zbmath.org/1541.811402024-09-27T17:47:02.548271Z"Plauschinn, Erik"https://zbmath.org/authors/?q=ai:plauschinn.erikSummary: In this note we study the mass spectrum of type IIB flux compactifications. We first give a general discussion of the mass matrix for F-term vacua in four-dimensional \(\mathcal{N} = 1\) supergravity theories and then specialize to type IIB Calabi-Yau orientifold compactifications in the presence of geometric and non-geometric fluxes. F-term vacua in this setting are in general \(\mathrm{AdS}_4\) vacua for which we compute the conformal dimensions of operators dual to the scalar fields. For the mirror-dual of the DGKT construction we find that one-loop corrections to the complex-structure moduli space lead to real-valued conformal dimensions -- only when ignoring these corrections we recover the integer values previously reported in the literature. For an example of a flux configurations more general than the DGKT mirror we also obtain non-integer conformal dimensions. Furthermore, we argue that stabilizing the axio-dilaton and complex-structure moduli in asymptotic regions of moduli space by fluxes implies that at least one of the corresponding mass eigenvalues diverges.Phases of a 10-D holographic hard wall modelhttps://zbmath.org/1541.811412024-09-27T17:47:02.548271Z"Singh, Akash"https://zbmath.org/authors/?q=ai:singh.akash"Yogendran, K. P."https://zbmath.org/authors/?q=ai:yogendran.k-pSummary: In this article, we study the finite temperature properties of a 10-D version of a hardwall model for QCD. Introducing fundamental matter via probe D7-branes and separate cutoffs \(r_m\) and \(r_g\) for the branes and the bulk, we present a detailed exploration of the phases for varying temperature and quark mass. Finite thermodynamic quantities are calculated using the procedure of holographic renormalization and used to characterize the phases. Finally, by fitting glueball and vector meson masses, we show how a unique phase diagram can be isolated.Three-point energy correlators and the celestial block expansionhttps://zbmath.org/1541.811422024-09-27T17:47:02.548271Z"Chang, Cyuan-Han"https://zbmath.org/authors/?q=ai:chang.cyuan-han"Simmons-Duffin, David"https://zbmath.org/authors/?q=ai:simmons-duffin.davidSummary: We study the three-point energy correlator (EEEC), defined as a matrix element of a product of three energy detectors at different locations on the celestial sphere. Lorentz symmetry implies that the EEEC can be decomposed into special functions called celestial blocks. We compute three-point celestial blocks in an expansion around the collinear limit, where the three detectors approach each other on the celestial sphere. The leading term is a traditional \(d - 2\)-dimensional four-point conformal block, and thus the collinear EEEC behaves like a conformally-invariant four-point function in \(d - 2\) dimensions. We obtain the coefficients of the conformal block decomposition for the collinear EEEC at leading nontrivial order in weakly-coupled \(\mathcal{N} = 4\) SYM and QCD. These data allow us to make certain all-orders predictions for the collinear EEEC in various kinematic limits, including the OPE limit and the double lightcone limit. We also study Ward identities satisfied by the EEEC and compute contact terms in the EEEC in weakly-coupled \(\mathcal{N} = 4\) SYM. Finally, we study the celestial block expansion of the EEEC in planar \(\mathcal{N} = 4\) SYM at strong coupling, determining celestial block coefficients to leading and first subleading order at large \(\lambda\).When does a three-dimensional Chern-Simons-Witten theory have a time reversal symmetry?https://zbmath.org/1541.811432024-09-27T17:47:02.548271Z"Geiko, Roman"https://zbmath.org/authors/?q=ai:geiko.roman"Moore, Gregory W."https://zbmath.org/authors/?q=ai:moore.gregory-wSummary: In this paper, we completely characterize time-reversal-invariant three-dimensional Chern-Simons gauge theories with torus gauge group. At the level of the Lagrangian, toral Chern-Simons theory is defined by an integral lattice, while at the quantum level, it is entirely determined by a quadratic function on a finite Abelian group and an integer mod 24. We find that quantum time-reversally symmetric theories can be defined by classical Lagrangians defined by integral lattices which have self-perpendicular embeddings into a unimodular lattice. We find that the quantum toral Chern-Simons theory admits a time-reversal symmetry iff the higher Gauss sums of the associated modular tensor category are real. We conjecture that the reality of the higher Gauss sums is necessary and sufficient for a general non-Abelian Chern-Simons to admit quantum T-symmetry.Usefulness of signed eigenvalue/vector distributions of random tensorshttps://zbmath.org/1541.811442024-09-27T17:47:02.548271Z"Kloos, Max Regalado"https://zbmath.org/authors/?q=ai:kloos.max-regalado"Sasakura, Naoki"https://zbmath.org/authors/?q=ai:sasakura.naokiSummary: Quantum field theories can be applied to compute various statistical properties of random tensors. In particular, signed distributions of tensor eigenvalues/vectors are the easiest, which can be computed as partition functions of four-fermi theories. Though signed distributions are different from genuine ones because of extra signs of weights, they are expected to coincide in vicinities of ends of distributions. In this paper, we perform a case study of the signed eigenvalue/vector distribution of the real symmetric order-three random tensor. The correct critical point and the correct end in the large \(N\) limit are obtained from the four-fermi theory, for which a method using the Schwinger-Dyson equation is very efficient. Since locations of ends are particularly important in applications, such as the largest eigenvalues and the best rank-one tensor approximations, signed distributions are the easiest and highly useful through the Schwinger-Dyson method.Chiral dualities for \(\mathrm{SQCD}_3\) with D-type superpotentialhttps://zbmath.org/1541.811452024-09-27T17:47:02.548271Z"Amariti, Antonio"https://zbmath.org/authors/?q=ai:amariti.antonio"Morgante, Davide"https://zbmath.org/authors/?q=ai:morgante.davideSummary: We study dualities for \(3d\) \(\mathrm{U}(N_c)_k\) \textit{chiral} SQCD with \(D_{n+2}\)-type superpotential, with \(n\) odd. We give a complete classification of such dualities in terms of the number of fundamentals and anti-fundamentals and the Chern-Simons level. The classification is obtained by real mass and Higgs flows from non-chiral dualities and we check the consistency of the new non-chiral dualities at the level of the partition function. We also check that the complex phases appearing in the integral identities between the partition functions are consistent with the contact terms computed as quantum corrections to the effective Chern-Simons level. The \(\mathrm{SU}(N_c)_k\) cases are recovered by gauging the topological symmetry from the \(\mathrm{U}(N_c)\) dualities. Finally, we consider the case of \(\mathrm{USp}(2N_c)_{2k}\) with two antisymmetric tensors and \(D_{n+2}\)-type superpotential.Interior analysis, stretched technique and bubbling geometrieshttps://zbmath.org/1541.811462024-09-27T17:47:02.548271Z"Jia, Qiuye"https://zbmath.org/authors/?q=ai:jia.qiuye"Lin, Hai"https://zbmath.org/authors/?q=ai:lin.hai.1Summary: We perform a detailed analysis of quarter BPS bubbling geometries with AdS asymptotics and their corresponding duality relations with their dual states in the quantum field theory side, among other aspects. We derive generalized Laplace-type equations with sources, obtained from linearized Monge-Ampere equations, and used for asymptotically AdS geometry. This enables us to obtain solutions specific to the asymptotically AdS context. We conduct a thorough analysis of boundary conditions and explore the stretched technique where boundary conditions are imposed on a stretched surface. These boundary conditions include grey droplets. This stretched technique is naturally used for the superstar, where we place grey droplet boundary conditions on the stretched surface. We also perform a coarse-graining of configurations and analyze the symplectic forms on the configuration space and their coarse-graining.Flow equation and fermion gap in the holographic superconductorshttps://zbmath.org/1541.811472024-09-27T17:47:02.548271Z"Yuk, Taewon"https://zbmath.org/authors/?q=ai:yuk.taewon"Sin, Sang-Jin"https://zbmath.org/authors/?q=ai:sin.sang-jinSummary: We reconsider the fermion spectral function in the presence of the Cooper pair condensation and identified the interaction type of complex scalar and fermion, which gives consistent results with the expected s-wave superconductor for the first time. We derive the matrix Riccati equation, which allows the precise calculation of the fermion spectral function. Apart from the gap structure, we studied the effect of the chemical potential and the density and compared it with the BCS theory. We found that two theories give similar results in small chemical potential but very different ones in the high-density case, which we attribute to the correlation effect.Holography and magnetohydrodynamics with dynamical gauge fieldshttps://zbmath.org/1541.811482024-09-27T17:47:02.548271Z"Ahn, Yong jun"https://zbmath.org/authors/?q=ai:ahn.yongjun"Baggioli, Matteo"https://zbmath.org/authors/?q=ai:baggioli.matteo"Huh, Kyoung-Bum"https://zbmath.org/authors/?q=ai:huh.kyoung-bum"Jeong, Hyun-Sik"https://zbmath.org/authors/?q=ai:jeong.hyun-sik"Kim, Keun-Young"https://zbmath.org/authors/?q=ai:kim.keun-young"Sun, Ya-Wen"https://zbmath.org/authors/?q=ai:sun.yawenSummary: Within the framework of holography, the Einstein-Maxwell action with Dirichlet boundary conditions corresponds to a dual conformal field theory in presence of an external gauge field. Nevertheless, in many real-world applications, e.g., magnetohydrodynamics, plasma physics, superconductors, etc. dynamical gauge fields and Coulomb interactions are fundamental. In this work, we consider bottom-up holographic models at finite magnetic field and (free) charge density in presence of dynamical boundary gauge fields which are introduced using mixed boundary conditions. We numerically study the spectrum of the lowest quasi-normal modes and successfully compare the obtained results to magnetohydrodynamics theory in \(2 + 1\) dimensions. Surprisingly, as far as the electromagnetic coupling is small enough, we find perfect agreement even in the large magnetic field limit. Our results prove that a holographic description of magnetohydrodynamics does not necessarily need higher-form bulk fields but can be consistently derived using mixed boundary conditions for standard gauge fields.Torus one-point correlation numbers in minimal Liouville gravityhttps://zbmath.org/1541.811492024-09-27T17:47:02.548271Z"Artemev, A."https://zbmath.org/authors/?q=ai:artemev.a-v.1|artemev.a-e|artemev.a-yu|artemev.aleksandr|artemev.andrei|artemev.a-a"Belavin, V."https://zbmath.org/authors/?q=ai:belavin.vladimir-aSummary: We present a method for the first principles calculation of tachyon one-point amplitudes in \((2, 2p + 1)\) minimal Liouville gravity defined on a torus. The method is based on the higher equations of motion in the Liouville CFT. These equations were earlier successfully applied for analytic calculations of the amplitudes in the spherical topology. We show that this approach allows to reduce the moduli integrals entering the definition of the torus amplitudes to certain boundary contributions, which can be calculated explicitly. The results agree with the calculations performed in the matrix models approach.Identifying large charge operatorshttps://zbmath.org/1541.811502024-09-27T17:47:02.548271Z"Badel, Gil"https://zbmath.org/authors/?q=ai:badel.gil"Monin, Alexander"https://zbmath.org/authors/?q=ai:monin.alexander"Rattazzi, Riccardo"https://zbmath.org/authors/?q=ai:rattazzi.riccardoSummary: The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge \(n^{-1}\), between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order \(n^{1/2}\) while the computation of observables is valid up to spins of order \(n\). Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.A dispersion relation for defect CFThttps://zbmath.org/1541.811512024-09-27T17:47:02.548271Z"Barrat, Julien"https://zbmath.org/authors/?q=ai:barrat.julien"Gimenez-Grau, Aleix"https://zbmath.org/authors/?q=ai:grau.aleix-gimenez"Liendo, Pedro"https://zbmath.org/authors/?q=ai:liendo.pedroSummary: We present a dispersion relation for defect CFT that reconstructs two-point functions in the presence of a defect as an integral of a single discontinuity. The main virtue of this formula is that it streamlines explicit bootstrap calculations, bypassing the resummation of conformal blocks. As applications we reproduce known results for monodromy defects in the epsilon-expansion, and present new results for the supersymmetric Wilson line at strong coupling in \(\mathcal{N} = 4\) SYM. In particular, we derive a new analytic formula for the highest \(R\)-symmetry channel of single-trace operators of arbitrary length.\(1/N\) expansion of the D3-D5 defect CFT at strong couplinghttps://zbmath.org/1541.811522024-09-27T17:47:02.548271Z"Beccaria, M."https://zbmath.org/authors/?q=ai:beccaria.matteo"Cabo-Bizet, A."https://zbmath.org/authors/?q=ai:cabo-bizet.alejandroSummary: We consider four dimensional \(\mathrm{U}(N)\) \(\mathcal{N} = 4\) SYM theory interacting with a 3d \(\mathcal{N} = 4\) theory living on a codimension-one interface and holographically dual to the D3-D5 system without flux. Localization captures several observables in this dCFT, including its free energy, related to the defect expectation value, and single trace \(\frac{1}{2}\)-BPS composite scalars. These quantities may be computed in a hermitian one-matrix model with non-polynomial single-trace potential. We exploit the integrable Volterra hierarchy underlying the matrix model and systematically study its \(1/N\) expansion at any value of the 't Hooft coupling. In particular, the strong coupling regime is determined -- up to non-perturbative exponentially suppressed corrections -- by differential relations that constrain higher order terms in the \(1/N\) expansion. The analysis is extended to the model with \(\mathrm{SU}(N)\) gauge symmetry by resorting to the more general Toda lattice equations.Exact thermal correlators of holographic \textit{CFT}shttps://zbmath.org/1541.811532024-09-27T17:47:02.548271Z"Bhatta, Atanu"https://zbmath.org/authors/?q=ai:bhatta.atanu"Mandal, Taniya"https://zbmath.org/authors/?q=ai:mandal.taniyaSummary: We compute the exact retarded Green's functions in thermal \textit{CFT}s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in AdS spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville \textit{CFT}. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary \textit{CFT}.Fractional conformal descendants and correlators in general 2D \(S_N\) orbifold CFTs at large \(N\)https://zbmath.org/1541.811542024-09-27T17:47:02.548271Z"Burrington, Benjamin A."https://zbmath.org/authors/?q=ai:burrington.benjamin-a"Peet, A. W."https://zbmath.org/authors/?q=ai:peet.amanda-wSummary: We consider correlation functions in symmetric product (\(S_N\)) orbifold CFTs at large \(N\) with arbitrary seed CFT. Specifically, we consider correlators of descendant operators constructed using both the full Virasoro generators \(L_m\) and fractional Virasoro generators \(\ell_{m/n_i}\). Using covering space techniques, we show that correlators of descendants may be written entirely in terms of correlators of ancestors, and further that the appropriate set of ancestors are those operators that lift to conformal primaries on the cover. We argue that the covering space data should cancel out in such calculations. To back this claim, we provide some example calculations by considering a three-point function of the form (4-cycle)-(2-cycle)-(5-cycle) that lifts to a three-point function of arbitrary primaries on the cover, and descendants thereof. In these examples we show that while the covering space is used for the calculation, the final descent relations do not depend on covering space data, nor on the details of which seed CFT is used to construct the orbifold, making these results universal.Larger twists and higher \(n\)-point functions with fractional conformal descendants in \(S_N\) orbifold CFTs at large \(N\)https://zbmath.org/1541.811552024-09-27T17:47:02.548271Z"Burrington, Benjamin A."https://zbmath.org/authors/?q=ai:burrington.benjamin-a"Peet, A. W."https://zbmath.org/authors/?q=ai:peet.amanda-wSummary: We consider correlation functions in symmetric product (\(S_N\)) orbifold CFTs at large \(N\) with arbitrary seed CFT, expanding on our earlier work [J. High Energy Phys. 2023, No. 2, Paper No. 91, 35 p. (2023; Zbl 1541.81154)]. Using covering space techniques, we calculate descent relations using fractional Virasoro generators in correlators, writing correlators of descendants in terms of correlators of ancestors. We first consider the case three-point functions of the form (\(m\)-cycle)-(\(n\)-cycle)-(\(q\)-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In these examples we show that the correlator descent relations make sense in the base space orbifold CFT, but do not depend on the specific details of the seed CFT. This makes these descent relations universal in all \(S_N\) orbifold CFTs. Next, we explore four-point functions of the form (2-cycle)-(\(n\)-cycle)-(\(n\)-cycle)-(2-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In such cases a single parameter in the map \(s\) parameterizes both the base space cross ratio \(\zeta_z\) and the covering space cross ratio \(\zeta_t\). We find that the correlator descent relations for the four point function make sense in the base space orbifold CFT as well, arguing that the dependence on the parameter \(s\) is tantamount to writing the descent relations in terms of the base space cross ratio. These descent relations again do not depend on the specifics of the seed CFT, making these universal as well.Interpolating boundary conditions on \(AdS_2\)https://zbmath.org/1541.811562024-09-27T17:47:02.548271Z"Canazas Garay, Anthonny F."https://zbmath.org/authors/?q=ai:canazas-garay.anthonny-f"Correa, Diego H."https://zbmath.org/authors/?q=ai:correa.diego-h"Faraggi, Alberto"https://zbmath.org/authors/?q=ai:faraggi.alberto"Silva, Guillermo A."https://zbmath.org/authors/?q=ai:silva.guillermo-aSummary: We consider two instances of boundary conditions for massless scalars on \(AdS_2\) that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full \(\mathrm{SL}(2; \mathbb{R})\) conformal group is not immediate given their non-local nature. To further clarify this issue, we compute holographically 2- and 4-point correlation functions using the aforementioned boundary conditions and study their transformation properties. Concretely, motivated by the dual description of some multi-parametric families of Wilson loops in ABJM theory, we look at the excitations of an open string around an \(AdS_2 \subset AdS_4 \times \mathbb{CP}^3\) worldsheet, thus obtaining correlators of operators inserted along a 1-dimensional defect in \(\mathcal{N} = 6\) super Chern-Simons-matter theory at strong coupling. Of the two types of boundary conditions analyzed, only one leads to the expected functional structure for conformal primaries; the other exhibits covariance under translations and rescalings but not under special conformal transformations.Shadow celestial amplitudeshttps://zbmath.org/1541.811572024-09-27T17:47:02.548271Z"Chang, Chi-Ming"https://zbmath.org/authors/?q=ai:chang.chi-ming"Cui, Wei"https://zbmath.org/authors/?q=ai:cui.wei.4|cui.wei"Ma, Wen-Jie"https://zbmath.org/authors/?q=ai:ma.wenjie"Shu, Hongfei"https://zbmath.org/authors/?q=ai:shu.hongfei"Zou, Hao"https://zbmath.org/authors/?q=ai:zou.haoSummary: We study scattering amplitudes in the shadow conformal primary basis, which satisfies the same defining properties as the original conformal primary basis and has many advantages over it. The shadow celestial amplitudes exhibit locality manifestly on the celestial sphere, and behave like correlation functions in conformal field theory under the operator product expansion (OPE) limit. We study the OPE limits for three-point shadow celestial amplitude, and general \(2 \rightarrow n - 2\) shadow celestial amplitudes from a certain class of Feynman diagrams. In particular, we compute the conformal block expansion of the \(s\)-channel four-point shadow celestial amplitude of massless scalars at tree-level, and show that the expansion coefficients factorize as products of OPE coefficients.Bootstrapping boundaries and braneshttps://zbmath.org/1541.811582024-09-27T17:47:02.548271Z"Collier, Scott"https://zbmath.org/authors/?q=ai:collier.scott"Mazáč, Dalimil"https://zbmath.org/authors/?q=ai:mazac.dalimil"Wang, Yifan"https://zbmath.org/authors/?q=ai:wang.yifan.3|wang.yifan.2|wang.yifanSummary: The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on \(AdS_3\).Thermalization and chaos in a 1+1d QFThttps://zbmath.org/1541.811592024-09-27T17:47:02.548271Z"Delacrétaz, Luca V."https://zbmath.org/authors/?q=ai:delacretaz.luca-v"Fitzpatrick, A. Liam"https://zbmath.org/authors/?q=ai:fitzpatrick.a-liam"Katz, Emanuel"https://zbmath.org/authors/?q=ai:katz.emanuel"Walters, Matthew T."https://zbmath.org/authors/?q=ai:walters.matthew-tSummary: We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors.On classification of fermionic rational conformal field theorieshttps://zbmath.org/1541.811602024-09-27T17:47:02.548271Z"Duan, Zhihao"https://zbmath.org/authors/?q=ai:duan.zhihao"Lee, Kimyeong"https://zbmath.org/authors/?q=ai:lee.kimyeong-m"Lee, Sungjay"https://zbmath.org/authors/?q=ai:lee.sungjay"Li, Linfeng"https://zbmath.org/authors/?q=ai:li.linfengSummary: We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principal congruence subgroup of \(\mathrm{PSL}(2, \mathbb{Z})\). The invariance strongly constrains the possible values of the central charge as well as the conformal weights in both Neveu-Schwarz and Ramond sectors, which improves the conventional holomorphic modular bootstrap method in a significant manner. This allows us to make much progress on the classification of fermionic rational conformal field theories with the number of independent characters less than five.The Gross-Neveu-Yukawa archipelagohttps://zbmath.org/1541.811612024-09-27T17:47:02.548271Z"Erramilli, Rajeev S."https://zbmath.org/authors/?q=ai:erramilli.rajeev-s"Iliesiu, Luca V."https://zbmath.org/authors/?q=ai:iliesiu.luca-v"Kravchuk, Petr"https://zbmath.org/authors/?q=ai:kravchuk.petr"Liu, Aike"https://zbmath.org/authors/?q=ai:liu.aike"Poland, David"https://zbmath.org/authors/?q=ai:poland.david"Simmons-Duffin, David"https://zbmath.org/authors/?q=ai:simmons-duffin.davidSummary: We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with \(O(N)\) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the \(O(N)\)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases \(N = 1, 2, 4, 8\), which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.Charge imbalance resolved Rényi negativity for free compact boson: two disjoint interval casehttps://zbmath.org/1541.811622024-09-27T17:47:02.548271Z"Gaur, Himanshu"https://zbmath.org/authors/?q=ai:gaur.himanshu"Yajnik, Urjit A."https://zbmath.org/authors/?q=ai:yajnik.urjit-aSummary: In this paper, we study the symmetry decomposition of Rényi negativity into charge imbalance sectors for the \(1+1\) dimensional free compact boson field with a global U(1) symmetry in the ground state for the case of two disjoint intervals. We obtain multicharged and charged Rényi negativity moments by computing the four-point correlator of flux-generating vertex operators on the Riemann surface. We then obtain charge imbalance resolved Rényi negativity by taking the Fourier transform of the charged moments. Finally, we match our results against the tight-binding model as a numerical check.Bootstrapping the effect of the twist operator in symmetric orbifold CFTshttps://zbmath.org/1541.811632024-09-27T17:47:02.548271Z"Guo, Bin"https://zbmath.org/authors/?q=ai:guo.bin.1"Hampton, Shaun D."https://zbmath.org/authors/?q=ai:hampton.shaun-dSummary: We study the 2D symmetric orbifold CFT of two copies of free bosons. The twist operator can join the two separated copies in the untwisted sector into a joined copy in the twisted sector. Starting with a state with any number of quanta in the untwisted sector, the state in the twisted sector obtained by the action of the twist operator can be computed by using the covering map method. We develop a new method to compute the effect of a twist operator by using the Bogoliubov ansatz and conformal symmetry. This may lead to more efficient tools to compute correlation functions involving twist operators.Fermions in boundary conformal field theory: crossing symmetry and \(\epsilon\)-expansionhttps://zbmath.org/1541.811642024-09-27T17:47:02.548271Z"Herzog, Christopher P."https://zbmath.org/authors/?q=ai:herzog.christopher-p"Schaub, Vladimir"https://zbmath.org/authors/?q=ai:schaub.vladimirSummary: We use the equations of motion in combination with crossing symmetry to constrain the properties of interacting fermionic boundary conformal field theories. This combination is an efficient way of determining operator product expansion coefficients and anomalous dimensions at the first few orders of the \(\epsilon\) expansion. Two necessary ingredients for this procedure are knowledge of the boundary and bulk spinor conformal blocks. The bulk spinor conformal blocks are derived here for the first time. We then consider a number of examples. For \(\phi\) a scalar field and \(\psi\) a fermionic field, we study the effects of a \(\phi\bar{\psi}\psi\) coupling in \(4 - \epsilon\) dimensions, a \(\phi^2\bar{\psi}\psi\) coupling in \(3 - \epsilon\) dimensions, and a \((\bar{\psi}\psi)^2\) coupling in \(2 + \epsilon\) dimensions. We are able to compute some new anomalous dimensions for operators in these theories. Finally, we relate the anomalous dimension of a surface operator to the behavior of the charge density near the surface.Pseudo entropy of primary operators in \(T\bar{T}/J\bar{T}\)-deformed CFTshttps://zbmath.org/1541.811652024-09-27T17:47:02.548271Z"He, Song"https://zbmath.org/authors/?q=ai:he.song"Yang, Jie"https://zbmath.org/authors/?q=ai:yang.jie.1|yang.jie.10|yang.jie.19|yang.jie.12|yang.jie.11|yang.jie.4|yang.jie.5|yang.jie.3|yang.jie.6|yang.jie.13|yang.jie.2"Zhang, Yu-Xuan"https://zbmath.org/authors/?q=ai:zhang.yuxuan"Zhao, Zi-Xuan"https://zbmath.org/authors/?q=ai:zhao.zixuanSummary: In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary operator quenches in 2D CFTs with \(T\bar{T}/J\bar{T}\)-deformation. Using perturbation theory, we analyze the corrections to the second pseudo-Rényi entropy at the late time, which exhibit a universal form, while its early-time behavior is model-dependent. Moreover, we uncover nontrivial time-dependent effects arising from the first-order deformation of the \(k^{\mathrm{th}}\) pseudo-Rényi entropy at the late time. Additionally, drawing inspiration from the gravitational side, specifically the gluing of two cutoff AdS geometries, we investigate the \(k^{\mathrm{th}}\) pseudo-Rényi entropy for vacuum states characterized by distinct \(T\bar{T}\)-deformation parameters, as well as for primary states acting on different deformed vacuum states. Our findings reveal additional corrections compared to the results of pseudo-Rényi entropy for globally deformed vacuum states.Celestial conformal collidershttps://zbmath.org/1541.811662024-09-27T17:47:02.548271Z"Hu, Yangrui"https://zbmath.org/authors/?q=ai:hu.yangrui"Pasterski, Sabrina"https://zbmath.org/authors/?q=ai:pasterski.sabrinaSummary: We start by observing that the light-ray operators featured in the conformal collider literature are celestial primaries. This allows us to rephrase the corresponding 4D CFT correlators as probing a conformally soft matter sector of the 2D celestial CFT (CCFT). To demonstrate the utility of this perspective we show how the recent \(w_{1+ \infty}\) symmetry observed in CCFT suggests a natural extension of the conformal collider operators.Celestial amplitudes in an ambidextrous basishttps://zbmath.org/1541.811672024-09-27T17:47:02.548271Z"Jorge-Diaz, Carmen"https://zbmath.org/authors/?q=ai:jorge-diaz.carmen"Pasterski, Sabrina"https://zbmath.org/authors/?q=ai:pasterski.sabrina"Sharma, Atul"https://zbmath.org/authors/?q=ai:sharma.atul-sSummary: We start by constructing a conformally covariant improvement of the celestial light transform which keeps track of the mixing between incoming and outgoing states under finite Lorentz transformations in \(\mathbb{R}^{2, 2}\). We then compute generic 2, 3 and 4-point celestial amplitudes for massless external states in the ambidextrous basis prepared by composing this \(\mathrm{SL}(2, \mathbb{R})\) intertwiner with the usual celestial map between momentum and boost eigenstates. The results are non-distributional in the celestial coordinates \((z, \bar{z})\) and conformally covariant in all scattering channels. Finally, we focus on the tree level 4-gluon amplitude where we present a streamlined route to the ambidextrous correlator based on Grassmannian formulae and examine its alpha space representation. In the process, we gain insights into the operator dictionary and CFT data of the holographic dual.Integrable field theories and their CCFT dualshttps://zbmath.org/1541.811682024-09-27T17:47:02.548271Z"Kapec, Daniel"https://zbmath.org/authors/?q=ai:kapec.daniel"Tropper, Adam"https://zbmath.org/authors/?q=ai:tropper.adamSummary: We compute the Mellin transforms of various two-dimensional integrable \(S\)-matrices, providing the first explicit, non-perturbative realizations of celestial CFT. In two dimensions, the Mellin transform is simply the Fourier transform in rapidity space, and the ``celestial correlator'' has no position dependence. The simplified setting allows us to study the analytic properties of CCFT correlators exactly as a function of the conformal dimensions. We find that the correlators exist as real distributions of the conformal weights, with asymptotics controlled by the mass spectrum and three-point couplings of the model. Coupling these models to a flat space limit of JT gravity preserves integrability and dresses the amplitudes by a rapidly varying gravitational phase. We find that the coupling to gravity smooths out certain singular aspects of the Mellin-transformed correlators.Two types of Witten zeta functionshttps://zbmath.org/1541.811692024-09-27T17:47:02.548271Z"Levin, A."https://zbmath.org/authors/?q=ai:levin.andrey-m"Olshanetsky, M."https://zbmath.org/authors/?q=ai:olshanetsky.mikhail-aSummary: We define two types of Witten's zeta functions according to Cartan's classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie group U. The type I Witten zeta functions, we introduce here, are related to the irreducible spherical representations of U. They arise in the harmonic analysis on compact symmetric spaces of the form U/K, where K is the maximal subgroup of U. To construct the type I zeta function we calculate the partition functions of 2d YM theory with broken gauge symmetry using the Migdal-Witten approach. We prove that for the rank one symmetric spaces the generating series for the values of the type I functions with integer arguments can be defined in terms of the generating series of the Riemann zeta-function.
{\copyright 2024 American Institute of Physics}On triality defects in 2d CFThttps://zbmath.org/1541.811702024-09-27T17:47:02.548271Z"Lu, Da-Chuan"https://zbmath.org/authors/?q=ai:lu.da-chuan"Sun, Zhengdi"https://zbmath.org/authors/?q=ai:sun.zhengdiSummary: We consider the triality fusion category discovered in the \(c = 1\) Kosterlitz-Thouless theory [\textit{R. Thorngren} and \textit{Y. Wang}, ``Fusion category symmetry II: categoriosities at \(c = 1\) and beyond'', Preprint, \url{arXiv:2106.12577}]. We analyze this fusion category using the tools from the group theoretical fusion category and compute the simple lines, fusion rules and \(F\)-symbols. We then studied the physical implication of this fusion category including deriving the spin selection rule, computing the asymptotic density of states of irreducible representations of the fusion category symmetries, and analyzing its anomaly and constraints under the renormalization group flow. There is another set of \(F\)-symbols for the fusion categories with the same fusion rule known in the literature [\textit{J. C. Y. Teo} et al., Ann. Phys. 360, 349--445 (2015; Zbl 1360.81242)]. We find these two solutions are different as they lead to different spin selection rules. This gives a complete list of the fusion categories with the same fusion rule by the classification result in [\textit{D. Jordan} and \textit{E. Larson}, ``On the classification of certain fusion categories'', Preprint, \url{arXiv:0812.1603}, see also Zbl 1208.18004].Modular linear differential equations for four-point sphere conformal blockshttps://zbmath.org/1541.811712024-09-27T17:47:02.548271Z"Mahanta, Ratul"https://zbmath.org/authors/?q=ai:mahanta.ratul"Sengupta, Tanmoy"https://zbmath.org/authors/?q=ai:sengupta.tanmoySummary: We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a connection between crossing transformations and modular transformations. We focus specifically on second order MLDEs with the cases of all identical and pairwise identical operators in the correlator. The central charge, the dimensions of the above operators and those of the intermediate ones are expressed in terms of parameters that occur in such MLDEs. In doing so, the \(q\)-expansions of the solutions to the MLDEs are compared with those of Virasoro blocks; hence, Zamolodchikov's elliptic recursion formula provides an important input. Using the actions of respective subgroups, bootstrap equations involving the associated 3-point coefficients have been set up and solved as well in terms of the MLDE parameters. We present explicit examples of MLDEs corresponding to BPZ and novel non-BPZ equations, as well as unitary and non-unitary CFTs.General light-cone gauge approach to conformal fields and applications to scalar and vector fieldshttps://zbmath.org/1541.811722024-09-27T17:47:02.548271Z"Metsaev, R. R."https://zbmath.org/authors/?q=ai:metsaev.r-rSummary: Totally symmetric arbitrary spin conformal fields propagating in the flat space of even dimension greater than or equal to four are studied. For such fields, we develop a general ordinary-derivative light-cone gauge formalism and obtain restrictions imposed by the conformal algebra symmetries on interaction vertices. We apply our formalism for the detailed study of conformal scalar and vector fields. For such fields, all parity-even cubic interaction vertices are obtained. The cubic vertices obtained are presented in terms of dressing operators and undressed vertices. We show that the undressed vertices of the conformal scalar and vector fields are equal, up to overall factor, to the cubic vertices of massless scalar and vector fields. Various conjectures about interrelations between the cubic vertices for conformal fields in conformal invariant theories and the cubic vertices for massless fields in Poincaré invariant theories are proposed.Bosonic rational conformal field theories in small genera, chiral fermionization, and symmetry/subalgebra dualityhttps://zbmath.org/1541.811732024-09-27T17:47:02.548271Z"Rayhaun, Brandon C."https://zbmath.org/authors/?q=ai:rayhaun.brandon-cSummary: A (1 + 1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple \((c, \mathcal{C})\) consisting of its central charge \(c\) and a unitary modular tensor category \(\mathcal{C}\) which describes the (2 + 1)D topological quantum field theory for which its maximally extended chiral algebra forms a holomorphic boundary condition. We establish a number of results pertaining to RCFTs in ``small'' genera, by which we informally mean genera with the central charge \(c\) and the number of primary operators \(\mathrm{rank}(\mathcal{C})\) both not too large. We start by completely solving the modular bootstrap problem for theories with at most four primary operators. In particular, we characterize, and provide an algorithm which efficiently computes, the function spaces to which the partition function of any bosonic RCFT with \(\mathrm{rank}(\mathcal{C})\leq4\) must belong. Using this result, and leveraging relationships between RCFTs and holomorphic vertex operator algebras which come from ``gluing'' and cosets, we rigorously enumerate all bosonic theories in 95 of the 105 genera \((c, \mathcal{C})\) with \(c \leq 24\) and \(\mathrm{rank}(\mathcal{C}) \leq 4\). This includes as (new) special cases the classification of chiral algebras with three primaries and \(c < 120/7 \sim 17.14\), and the classification of chiral algebras with four primaries and \(c < 62/3 \sim 20.67\). We then study two applications of our classification. First, by making use of chiral versions of bosonization and fermionization, we obtain the complete list of purely left-moving fermionic RCFTs with \(c < 23\) as a corollary of the results of the previous paragraph. Second, using a (conjectural) concept which we call ``symmetry/subalgebra duality,'' we precisely relate our bosonic classification to the problem of determining certain generalized global symmetries of holomorphic vertex operator algebras.
{\copyright 2024 American Institute of Physics}Engineering small flux superpotentials and mass hierarchieshttps://zbmath.org/1541.811742024-09-27T17:47:02.548271Z"Bastian, Brice"https://zbmath.org/authors/?q=ai:bastian.brice"Grimm, Thomas W."https://zbmath.org/authors/?q=ai:grimm.thomas-w"van de Heisteeg, Damian"https://zbmath.org/authors/?q=ai:van-de-heisteeg.damianSummary: We study the stabilization of complex structure moduli in Type IIB flux compactifications by using recent general results about the form of the superpotential and Kähler potential near the boundaries of the moduli space. In this process we show how vacua with an exponentially small vacuum superpotential can be realized systematically and understood conceptually within asymptotic Hodge theory. We distinguish two types of vacua realizing such superpotentials that differ by the mass scales of the stabilized moduli. Masses polynomially depending on the moduli arise if the superpotential contains exponential corrections whose existence is required to ensure the non-degeneracy of the moduli space metric. We use the fact that such essential corrections are controlled by asymptotic Hodge theory and have recently been constructed for all one- and two-moduli asymptotic regimes. These insights allow us to obtain new vacua near boundaries in complex structure moduli space that include Seiberg-Witten points. In these examples we find that the scale of the vacuum superpotential can be bounded from below through the exponential of the negative D3-brane tadpole.Callan-Rubakov effect and higher charge monopoleshttps://zbmath.org/1541.811752024-09-27T17:47:02.548271Z"Brennan, T. Daniel"https://zbmath.org/authors/?q=ai:brennan.t-danielSummary: In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole's magnetic field polarizes the fermions into purely in-going and out-going modes. Consistency requires that the UV fermion-monopole interaction leads to non-trivial IR boundary conditions that relate the in-going to out-going modes. These non-trivial boundary conditions lead to what is known as the Callan-Rubakov effect. Here we derive the effective boundary condition by explicitly integrating out the UV degrees of freedom for the general class of spherically symmetric \(\mathrm{SU}(N)\) monopoles coupled to massless fermions of arbitrary representation. We then show that the boundary conditions preserve symmetries without ABJ-type anomalies. As an application we explicitly derive the boundary conditions for the stable, spherically symmetric monopoles associated to the SU(5) Georgi-Glashow model and comment on the relation to baryon number violation.Symmetry TFTs for 3d QFTs from M-theoryhttps://zbmath.org/1541.811762024-09-27T17:47:02.548271Z"van Beest, Marieke"https://zbmath.org/authors/?q=ai:van-beest.marieke"Gould, Dewi S. W."https://zbmath.org/authors/?q=ai:gould.dewi-s-w"Schäfer-Nameki, Sakura"https://zbmath.org/authors/?q=ai:schafer-nameki.sakura"Wang, Yi-Nan"https://zbmath.org/authors/?q=ai:wang.yinanSummary: We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their 't Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold \(Y_7\), which either is the link of a conical Calabi-Yau four-fold or part of an \(\mathrm{AdS}_4 \times Y_7\) holographic solution. In the holographic setting we first consider the 3d \(\mathcal{N} = 6\) ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d \(\mathcal{N} = 2\) quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type \(Y_7 = Y^{p, k}(\mathbb{CP}^2)\). The SymTFT encodes 0- and 1-form symmetries, as well as potential 't Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for U(1) Chern-Simons terms in the dual field theory.Anomalous and axial \(Z^\prime\) contributions to \(g - 2\)https://zbmath.org/1541.811772024-09-27T17:47:02.548271Z"Anastasopoulos, Pascal"https://zbmath.org/authors/?q=ai:anastasopoulos.pascal"Kaneta, Kunio"https://zbmath.org/authors/?q=ai:kaneta.kunio"Kiritsis, Elias"https://zbmath.org/authors/?q=ai:kiritsis.elias-b"Mambrini, Yann"https://zbmath.org/authors/?q=ai:mambrini.yannSummary: We study the effects of an anomalous \(Z^\prime\) boson on the anomalous magnetic moment of the muon (\(g - 2\)), and especially the impact of its axial coupling. We mainly evaluate the \textit{negative} contribution to (\(g - 2\)) of such couplings at one-loop and look at the anomalous couplings generated at two loops. We find areas of the parameter space, where the anomalous contribution becomes comparable and even dominant compared to the one-loop contribution. We show that in such cases, the cutoff of the theory is sufficiently low, so that new charged fermions can be found in the next round of collider experiments. We comment on the realization of such a context in string theory orientifolds.Gauge invariance and finite counterterms in chiral gauge theorieshttps://zbmath.org/1541.811782024-09-27T17:47:02.548271Z"Cornella, Claudia"https://zbmath.org/authors/?q=ai:cornella.claudia"Feruglio, Ferruccio"https://zbmath.org/authors/?q=ai:feruglio.ferruccio"Vecchi, Luca"https://zbmath.org/authors/?q=ai:vecchi.lucaSummary: We derive the finite one-loop counterterm required to restore the Ward Identities broken by the regularization scheme in chiral gauge theories. Our result is an analytic expression applicable to a wide class of regularizations satisfying a few general properties. We adopt the background field method, which ensures background gauge invariance in the quantized theory, and focus on renormalizable chiral theories with arbitrary gauge group and fermions in general representations. Our approach can be extended to theories involving scalars, such as the Standard Model, or to non-renormalizable theories, such as the SMEFT. As a concrete application, we work out the finite counterterm at one loop in the Standard Model, within dimensional regularization and the Breitenlohner-Maison-'t Hooft-Veltman prescription for \(\gamma_5\).One-loop string amplitudes in \(\mathrm{AdS}_5\times\mathrm{S}^5\): Mellin space and sphere splittinghttps://zbmath.org/1541.811792024-09-27T17:47:02.548271Z"Aprile, F."https://zbmath.org/authors/?q=ai:aprile.francesco"Drummond, J. M."https://zbmath.org/authors/?q=ai:drummond.james-m"Glew, R."https://zbmath.org/authors/?q=ai:glew.r"Santagata, M."https://zbmath.org/authors/?q=ai:santagata.maria-cSummary: We study string corrections to one-loop amplitudes of single-particle operators \(\mathcal{O}_p\) in \(\mathrm{AdS}_5\times\mathrm{S}^5\). The tree-level correlators in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges \(p_{i=1, 2, 3, 4}\). The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion.
Here we present a closed-form Mellin space formula for \(\langle\mathcal{O}_{p1}\mathcal{O}_{p2}\mathcal{O}_{p3}\mathcal{O}_{p4}\rangle\) at order \((\alpha^\prime)^3\), valid for arbitrary external charges \(p_i\). Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as `sphere splitting'. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the \(\mathrm{AdS}_5\times\mathrm{S}^5\) amplitude, our one-loop amplitude naturally splits the \(S^5\) part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large \(p\) limit.Large \(N\) superconformal indices for 3d holographic SCFTshttps://zbmath.org/1541.811802024-09-27T17:47:02.548271Z"Bobev, Nikolay"https://zbmath.org/authors/?q=ai:bobev.nokolai"Choi, Sunjin"https://zbmath.org/authors/?q=ai:choi.sunjin"Hong, Junho"https://zbmath.org/authors/?q=ai:hong.junho"Reys, Valentin"https://zbmath.org/authors/?q=ai:reys.valentinSummary: We study a limit of the superconformal index of the ABJM theory on \(S^1 \times S^2\) in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the \(1/N\) expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d \(\mathcal{N} = 4\) SYM coupled to one adjoint and \(N_f\) fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in \(\mathrm{AdS}_4\).Large \(N\) partition functions of the ABJM theoryhttps://zbmath.org/1541.811812024-09-27T17:47:02.548271Z"Bobev, Nikolay"https://zbmath.org/authors/?q=ai:bobev.nokolai"Hong, Junho"https://zbmath.org/authors/?q=ai:hong.junho"Reys, Valentin"https://zbmath.org/authors/?q=ai:reys.valentinSummary: We study the large \(N\) limit of some supersymmetric partition functions of the \(\mathrm{U}(N)_k\times\mathrm{U}(N)_{-k}\) ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in the large \(N\) limit, for the partition function on the \(\mathrm{U}(1)\times\mathrm{U}(1)\) invariant squashed sphere in the presence of real masses in terms of an Airy function. Several non-trivial tests of this conjecture are presented. In addition, we derive an explicit compact expression for the topologically twisted index of the ABJM theory valid at fixed \(k\) to all orders in the \(1/N\) expansion. We use these results to derive the topologically twisted index and the sphere partition function in the 't Hooft limit which correspond to genus g type IIA string theory free energies to all orders in the \(\alpha^\prime\) expansion. We discuss the implications of our results for holography and the physics of \(\mathrm{AdS}_4\) black holes.Erratum to: ``4D supersymmetric gauge theories of spacetime translations''https://zbmath.org/1541.811822024-09-27T17:47:02.548271Z"Brandt, Friedemann"https://zbmath.org/authors/?q=ai:brandt.friedemannErratum to the author's paper [ibid. 2022, No. 10, Paper No. 21, 33 p. (2022; Zbl 1534.81161)].Addendum to: ``4D supersymmetric gauge theories of spacetime translations''https://zbmath.org/1541.811832024-09-27T17:47:02.548271Z"Brandt, Friedemann"https://zbmath.org/authors/?q=ai:brandt.friedemannFrom the text: In this addendum to the author's previous paper [ibid. 2022, No. 10, Paper No. 21, 33 p. (2022; Zbl 1534.81161)] it is shown that the theories presented in section 4.3 of [loc. cit.] exhaust, modulo field redefinitions, all supersymmetric theories which are in the scope of investigation of [loc. cit.]. More precisely it is shown that every supersymmetric theory in this scope of investigation is a theory as in section 4.3 of [loc. cit.] or can be obtained from one of these theories by a local field redefinition of the fermionic fields.Poles at infinity in on-shell diagramshttps://zbmath.org/1541.811842024-09-27T17:47:02.548271Z"Brown, Taro V."https://zbmath.org/authors/?q=ai:brown.taro-v"Oktem, Umut"https://zbmath.org/authors/?q=ai:oktem.umut"Trnka, Jaroslav"https://zbmath.org/authors/?q=ai:trnka.jaroslavSummary: In this paper we study on-shell diagrams in \(\mathcal{N} < 4\) supersymmetric Yang-Mills (SYM) theory. These are on-shell gauge invariant objects which appear as cuts of loop integrands in the context of generalized unitarity and serve as building blocks for amplitudes in recursion relations. In the dual formulation, they are associated with cells of the positive Grassmannian \(G_+(k, n)\) and the on-shell functions can be reproduced as canonical differential forms. While for the case of the \(\mathcal{N} = 4\) maximally supersymmetric Yang-Mills theory all poles in on-shell diagrams correspond to IR poles when the momentum flows in edges are zero, for \(\mathcal{N} < 4\) SYM theories there are new UV poles when the loop momenta go to infinity. These poles originate from the prefactor of the canonical dlog form and do not correspond to erasing edges in on-shell diagrams. We show that they can be interpreted as a diagrammatic operation which involves pinching a loop and performing a ``non-planar twist'' on external legs, which gives rise to a non-planar on-shell diagram. Our result provides an important clue on the role of poles at infinite momenta in on-shell scattering amplitudes, and the relation to non-planar on-shell functions.Type II double field theory in superspacehttps://zbmath.org/1541.811852024-09-27T17:47:02.548271Z"Butter, Daniel"https://zbmath.org/authors/?q=ai:butter.danielSummary: We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group \(\mathrm{OSp}(10, 10|64)\), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic double field theory, the local tangent space must be enhanced from the double Lorentz group in order to eliminate unphysical components of the supervielbein and to define covariant torsion and curvature tensors. This leads to an infinite hierarchy of local tangent space symmetries, which are connected to the super-\(\mathrm{Maxwell}_\infty\) algebra. A novel feature of type II is the Ramond-Ramond sector, which can be encoded as an orthosymplectic spinor (encoding the complex of super \(p\)-forms in conventional superspace). Its covariant field strength bispinor itself appears as a piece of the supervielbein. We provide a concise discussion of the superspace Bianchi identities through dimension two and show how to recover the component supersymmetry transformations of type II DFT. In addition, we show how the democratic formulation of type II superspace may be recovered by gauge-fixing.On the 4d superconformal index near roots of unity: bulk and localized contributionshttps://zbmath.org/1541.811862024-09-27T17:47:02.548271Z"Cabo-Bizet, Alejandro"https://zbmath.org/authors/?q=ai:cabo-bizet.alejandroSummary: We study the expansion near roots of unity of the superconformal index of 4d \(\mathrm{SU}(N)\) \(\mathcal{N} = 4\) SYM. In such an expansion, middle-dimensional walls of non-analyticity are shown to emerge in the complex analytic extension of the integrand. These walls intersect the integration contour at infinitesimal vicinities and come from both, the vector and chiral multiplet contributions, and combinations thereof. We will call these intersections \textit{vector} and \textit{chiral bits}, and the complementary region \textit{bulk}, and show that, in the corresponding limit, the integrals along the infinitesimal bits include, among other contributions, factorized products of either Chern-Simons and 3d topologically twisted partition functions.
In particular, we find that the leading asymptotic contribution to the index, which comes from collecting all contributions coming from vector bits, reduces to an average over a set of \(N\) copies of three-dimensional \(\mathrm{SU}(N)\) Chern-Simons partition functions in Lens spaces \(L(m, 1)\) with \(m > 1\), in the presence of background \(\mathbb{Z}_m^{N-1}\) flat connections. The average is taken over the background connections, which are the positions of individual vector bits along the contour. We also find there are other subleading contributions, a finite number of them at finite \(N\), which include averages over products of Chern-Simons and/or topologically \(A\)-twisted Chern-Simons-matter partition functions in three-dimensional manifolds. This shows how in certain limits the index of 4d \(\mathrm{SU}(N)\) \(\mathcal{N} = 4\) SYM organizes, \textit{via} an unambiguously defined coarse graining procedure, into \textit{averages} over a finite number of lower dimensional theories.Bootstrapping \(\mathcal{N} = 4\) sYM correlators using integrabilityhttps://zbmath.org/1541.811872024-09-27T17:47:02.548271Z"Caron-Huot, Simon"https://zbmath.org/authors/?q=ai:caron-huot.simon"Coronado, Frank"https://zbmath.org/authors/?q=ai:coronado.frank"Trinh, Anh-Khoi"https://zbmath.org/authors/?q=ai:trinh.anh-khoi"Zahraee, Zahra"https://zbmath.org/authors/?q=ai:zahraee.zahraSummary: How much spectral information is needed to determine the correlation functions of a conformal theory? We study this question in the context of planar supersymmetric Yang-Mills theory, where integrability techniques accurately determine the single-trace spectrum at finite 't Hooft coupling. Corresponding OPE coefficients are constrained by dispersive sum rules, which implement crossing symmetry. Focusing on correlators of four stress-tensor multiplets, we construct combinations of sum rules which determine one-loop correlators, and we study a numerical bootstrap problem that nonperturbatively bounds planar OPE coefficients. We observe interesting cusps at the location of physical operators, and we obtain a nontrivial upper bound on the OPE coefficient of the Konishi operator outside the perturbative regime.Spinor-helicity formalism for massive and massless amplitudes in five dimensionshttps://zbmath.org/1541.811882024-09-27T17:47:02.548271Z"Chiodaroli, Marco"https://zbmath.org/authors/?q=ai:chiodaroli.marco"Günaydin, Murat"https://zbmath.org/authors/?q=ai:guenaydin.murat"Johansson, Henrik"https://zbmath.org/authors/?q=ai:johansson.henrik"Roiban, Radu"https://zbmath.org/authors/?q=ai:roiban.raduSummary: Five-dimensional gauge and gravity theories are known to exhibit striking properties. \(D = 5\) is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor theories. Five-dimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level.
In this paper, we take a step towards the systematic investigation of amplitudes in five dimensions, and present a five-dimensional version of the spinor-helicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for on-shell spinor and polarization variables such that the little-group symmetry and gauge redundancy are manifest. Massive self-dual tensor states are discussed in some detail, as well as all the on-shell supermultiplets that can appear in matter-coupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless ten-dimensional Majorana-Weyl spinors as products of five-dimensional massive spinors.
We present compact expressions for superamplitudes at multiplicity three and four, including several novel superamplitudes that either do not straightforwardly uplift to six dimensions, or have not appeared in the six-dimensional literature. We discuss several examples of five-dimensional double-copy constructions in the context of gravitational theories with massive vectors and tensors, illustrating that the formalism we construct can also be used to considerably streamline the double-copy construction of \(\mathcal{N} = 2\) Maxwell-Einstein supergravities.\( \mathcal{N} = 4\) SYM, (super)-polynomial rings and emergent quantum mechanical symmetrieshttps://zbmath.org/1541.811892024-09-27T17:47:02.548271Z"de Mello Koch, Robert"https://zbmath.org/authors/?q=ai:de-mello-koch.robert"Ramgoolam, Sanjaye"https://zbmath.org/authors/?q=ai:ramgoolam.sanjayeSummary: The structure of half-BPS representations of \(\mathrm{psu}(2, 2|4)\) leads to the definition of a super-polynomial ring \(\mathcal{R}(8|8)\) which admits a realisation of \(\mathrm{psu}(2, 2|4)\) in terms of differential operators on the super-ring. The character of the half-BPS fundamental field representation encodes the resolution of the representation in terms of an exact sequence of modules of \(\mathcal{R}(8|8)\). The half-BPS representation is realized by quotienting the super-ring by a quadratic ideal, equivalently by setting to zero certain quadratic polynomials in the generators of the super-ring. This description of the half-BPS fundamental field irreducible representation of \(\mathrm{psu}(2, 2|4)\) in terms of a super-polynomial ring is an example of a more general construction of lowest-weight representations of Lie (super-) algebras using polynomial rings generated by a commuting subspace of the standard raising operators, corresponding to positive roots of the Lie (super-) algebra. We illustrate the construction using simple examples of representations of su(3) and su(4). These results lead to the definition of a notion of quantum mechanical emergence for oscillator realisations of symmetries, which is based on ideals in the ring of polynomials in the creation operators.On extended supersymmetry of 4d Galileons and 3-brane effective actionshttps://zbmath.org/1541.811902024-09-27T17:47:02.548271Z"Elvang, Henriette"https://zbmath.org/authors/?q=ai:elvang.henriette"Mitchell, Matthew Dominique"https://zbmath.org/authors/?q=ai:mitchell.matthew-dominiqueSummary: We use on-shell amplitude methods to systematically analyze the possibility of extended supersymmetry for 4d Galileon models, expanding on previous \(\mathcal{N} = 1\) results. Assuming spins \(\leq 1\), we prove that there exists no \(\mathcal{N} = 4\) supersymmetric extension of 4d Galileons with a single vector multiplet. Thus the Galileons cannot be part of the effective action of a single flat maximally supersymmetric D3-brane, and that explains why such terms do not appear in the \(\alpha^\prime\)-expansion of the abelian open superstring amplitude. For \(\mathcal{N} = 2\) Galileons, we show that the complex scalar \(Z = \phi + i\chi\) of the vector supermultiplet cannot have \(\phi\) and \(\chi\) both enjoy enhanced shift symmetry; instead, \(\chi\) can at best be an \(R\)-axion with constant shift symmetry. Using the soft bootstrap, we demonstrate that the quartic DBI-Galileon is incompatible with \(\mathcal{N} = 2\) supersymmetry. A similar analysis performed at 7-point shows that a 2-parameter family of \(\mathcal{N} = 2\) supersymmetric quintic Galileons coupled with DBI passes the soft bootstrap. Finally, we show how supersymmetric couplings between Galileons and gravitons arise in generalizations of our constructions, and we conclude with a discussion of Galileons and DBI-Galileons in the context of UV-completability vs. the Swampland.Constant primary operators and where to find them: the strange case of BPS defects in ABJ(M) theoryhttps://zbmath.org/1541.811912024-09-27T17:47:02.548271Z"Gorini, Nicola"https://zbmath.org/authors/?q=ai:gorini.nicola"Griguolo, Luca"https://zbmath.org/authors/?q=ai:griguolo.luca"Guerrini, Luigi"https://zbmath.org/authors/?q=ai:guerrini.luigi"Penati, Silvia"https://zbmath.org/authors/?q=ai:penati.silvia"Seminara, Domenico"https://zbmath.org/authors/?q=ai:seminara.domenico"Soresina, Paolo"https://zbmath.org/authors/?q=ai:soresina.paoloSummary: We investigate the one-dimensional defect SCFT defined on the 1/2 BPS Wilson line/loop in ABJ(M) theory. We show that the supermatrix structure of the defect imposes a covariant supermatrix representation of the supercharges. Exploiting this covariant formulation, we prove the existence of a long multiplet whose highest weight state is a constant supermatrix operator. At weak coupling, we study this operator in perturbation theory and confirm that it acquires a non-trivial anomalous dimension. At strong coupling, we conjecture that this operator is dual to the lowest bound state of fluctuations of the fundamental open string in \(\mathrm{AdS}_4\times\mathbb{CP}_3\) around the classical 1/2 BPS solution. Quite unexpectedly, this operator also arises in the cohomological equivalence between bosonic and fermionic Wilson loops. We also discuss some regularization subtleties arising in perturbative calculations on the infinite Wilson line.The two-loop eight-point amplitude in ABJM theoryhttps://zbmath.org/1541.811922024-09-27T17:47:02.548271Z"He, Song"https://zbmath.org/authors/?q=ai:he.song"Huang, Yu-tin"https://zbmath.org/authors/?q=ai:huang.yu-tin"Kuo, Chia-Kai"https://zbmath.org/authors/?q=ai:kuo.chia-kai"Li, Zhenjie"https://zbmath.org/authors/?q=ai:li.zhenjieSummary: In this paper, we present the two-loop correction to scattering amplitudes in three-dimensional \(\mathcal{N} = 6\) Chern-Simons matter theory. We use the eight-point case as our main example, but the method generalizes to all multiplicities. The integrand is completely fixed by dual conformal symmetry, maximal cuts, constraints from soft-collinear behavior, and from the vanishing of odd-multiplicity amplitudes. After performing integrations with Higgs regularizations, the integrated results demonstrate that the infrared divergence is again identical to that of \(\mathcal{N} = 4\) super Yang-Mills. After subtracting divergences, the finite part is dual conformal invariant, and respects various symmetries; it has uniform transcendentality weight two and exhibits a nice analytic structure.Chiral spectrum of the universal tuned \((\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1))/\mathbb{Z}_6\) 4D F-theory modelhttps://zbmath.org/1541.811932024-09-27T17:47:02.548271Z"Jefferson, Patrick"https://zbmath.org/authors/?q=ai:jefferson.patrick"Taylor, Washington"https://zbmath.org/authors/?q=ai:taylor.washington-iv"Turner, Andrew P."https://zbmath.org/authors/?q=ai:turner.andrew-pSummary: We use the recently developed methods of \textit{P. Jefferson} et al. [``Chiral matter multiplicities and resolution-independent structure in 4D F-theory models'', Preprint, \url{arXiv:2108.07810}] to analyze vertical flux backgrounds and associated chiral matter spectra in the 4D universal \((\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1))/\mathbb{Z}_6\) model introduced in [\textit{N. Raghuram} et al.,``General F-theory models with tuned \((\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1))/\mathbb{Z}_6\) symmetry'', Preprint, \url{arXiv:1912.10991}], which is believed to describe the most generic family of F-theory vacua with tuned (\(\mathrm{SU}(3) \times\mathrm{SU}(2)\times\mathrm{U}(1))/\mathbb{Z}_6\) gauge symmetry. Our analysis focuses on a resolution of a particular presentation of the (\(\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1))/\mathbb{Z}_6\) model in which the elliptic fiber is realized as a cubic in \(\mathbb{P}^2\) fibered over an arbitrary smooth threefold base. We show that vertical fluxes can produce nonzero multiplicities for all chiral matter families that satisfy 4D anomaly cancellation, which include as a special case the chiral matter families of the Minimal Supersymmetric Standard Model.Ginzburg-Landau description and emergent supersymmetry of the \((3, 8)\) minimal modelhttps://zbmath.org/1541.811942024-09-27T17:47:02.548271Z"Klebanov, Igor R."https://zbmath.org/authors/?q=ai:klebanov.igor-r"Narovlansky, Vladimir"https://zbmath.org/authors/?q=ai:narovlansky.vladimir"Sun, Zimo"https://zbmath.org/authors/?q=ai:sun.zimo"Tarnopolsky, Grigory"https://zbmath.org/authors/?q=ai:tarnopolsky.grigory-mSummary: A pair of the 2D non-unitary minimal models \(M(2, 5)\) is known to be equivalent to a variant of the \(M(3, 10)\) minimal model. We discuss the RG flow from this model to another non-unitary minimal model, \(M(3, 8)\). This provides new evidence for its previously proposed Ginzburg-Landau description, which is a \(\mathbb{Z}_2\) symmetric theory of two scalar fields with cubic interactions. We also point out that \(M(3, 8)\) is equivalent to the \((2, 8)\) superconformal minimal model with the diagonal modular invariant. Using the 5-loop results for theories of scalar fields with cubic interactions, we exhibit the \(6 - \epsilon\) expansions of the dimensions of various operators. Their extrapolations are in quite good agreement with the exact results in 2D. We also use them to approximate the scaling dimensions in \(d = 3, 4, 5\) for the theories in the \(M(3, 8)\) universality class.A novel solution to the gravitino problemhttps://zbmath.org/1541.811952024-09-27T17:47:02.548271Z"Qiu, Yu-Cheng"https://zbmath.org/authors/?q=ai:qiu.yu-cheng"Tye, S.-H. Henry"https://zbmath.org/authors/?q=ai:tye.s-h-henrySummary: In a general phenomenological model with local supersymmetry, the amount of massive gravitinos produced in early universe tends to violate the known dark matter density bound by many orders of magnitude. In the brane world scenario in Type IIB string theory, we propose a novel way to evade this problem. There, the standard model of strong and electroweak interactions live inside the anti-D3-branes (\(\overline{\mathrm{D}3}\)-branes) that span the 3 large spatial dimensions. Here, the ``potential'' Goldstino to be absorbed by the gravitino (to become massive) is the fermion component of the open string nilpotent superfield \(X\) (i.e., \(X^2 = 0\)) which is present only inside the \(\overline{\mathrm{D}3}\)-branes. This non-linear supergravity scenario offers 2 ways to solve the gravitino problem, with very different particle physics phenomenologies: (1) To satisfy the necessary condition for a naturally small cosmological constant \(\Lambda\), the supersymmetry breaking \(\overline{\mathrm{D}3}\)-branes tension is precisely cancelled by the Higgs spontaneous symmetry breaking effect, so the gravitino is ultra-light and its contribution to the dark matter density is negligible. If exist, the super-particles should have already been detected in experiments. To avoid contradiction with their non-observation, \(X\) is applied to project out all the ``R-parity odd'' fields. Consequently, this non-linear supergravity model is almost identical to the standard model. (2) As an alternative, one can have a massive gravitino (e.g., \(\hat{m}_{3/2} > 100\) GeV) due to the supersymmetry breaking tension of the \(\overline{\mathrm{D}3}\)-branes. Here, the super-particles can be heavy enough to have avoided detection so far. Since the open string Goldstino exists only inside the \(\overline{\mathrm{D}3}\)-branes, the gravitino is heavy only inside the \(\overline{\mathrm{D}3}\)-branes, but massless or ultra-light outside the \(\overline{\mathrm{D}3}\)-branes. This means that the gravitinos will be pushed out of the \(\overline{\mathrm{D}3}\)-branes to the extra dimensions in the bulk, a phenomenon analogous to the Meissner effect for the massive photons inside super-conductors but massless outside. As a result, the massive gravitinos will be depleted so the gravitino problem is absent. In this case, a fine-tuning is necessary to obtain the very small observed \(\Lambda_{\mathrm{obs}}\).Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theoryhttps://zbmath.org/1541.811962024-09-27T17:47:02.548271Z"Benini, Marco"https://zbmath.org/authors/?q=ai:benini.marco.1"Musante, Giorgio"https://zbmath.org/authors/?q=ai:musante.giorgio"Schenkel, Alexander"https://zbmath.org/authors/?q=ai:schenkel.alexanderSummary: We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of \(m\)-dimensional globally hyperbolic Lorentzian manifolds. Our comparison is realized as an explicit isomorphism of time-orderable prefactorization algebras. The key ingredients of our approach are the retarded and advanced Green's homotopies associated with free BV theories, which generalize retarded and advanced Green's operators to cochain complexes of linear differential operators.Dressed vs. pairwise states, and the geometric phase of monopoles and chargeshttps://zbmath.org/1541.811972024-09-27T17:47:02.548271Z"Csáki, Csaba"https://zbmath.org/authors/?q=ai:csaki.csaba"Dong, Zi-Yu"https://zbmath.org/authors/?q=ai:dong.zi-yu"Telem, Ofri"https://zbmath.org/authors/?q=ai:telem.ofri"Terning, John"https://zbmath.org/authors/?q=ai:terning.john"Yankielowicz, Shimon"https://zbmath.org/authors/?q=ai:yankielowicz.shimonSummary: We construct the Faddeev-Kulish dressed multiparticle states of electrically and magnetically charged particles, incorporating the effects of real and virtual soft photons. We calculate the properties of such dressed states under Lorentz transformations, and find that they can be identified with the pairwise multi-particle states that transform under the pairwise little group. The shifts in the dressing factors under Lorentz transformations are finite and have a simple geometric interpretation. Using the transformation properties of the dressed states we also present a novel, fully quantum field theoretic derivation of the geometric (Berry) phase obtained by an adiabatic rotation of the Dirac string, and also of the Dirac quantization condition. For half integer pairwise helicity, we show that these multiparticle states have flipped spin-statistics, reproducing the surprising fact that fermions can be made out of bosons.Wolfes model \textit{aka} \(G_2/I_6\)-rational integrable model: \(g^{(2)}\), \(g^{(3)}\) hidden algebras and quartic polynomial algebra of integralshttps://zbmath.org/1541.811982024-09-27T17:47:02.548271Z"Lopez Vieyra, Juan Carlos"https://zbmath.org/authors/?q=ai:lopez-vieyra.juan-carlos"Turbiner, Alexander V."https://zbmath.org/authors/?q=ai:turbiner.alexanderSummary: One-dimensional 3-body Wolfes model with 2- and 3-body interactions also known as \(G_2/I_6\)-rational integrable model of the Hamiltonian reduction is exactly-solvable and superintegrable. Its Hamiltonian \(H\) and two integrals \(\mathcal{I}_1\), \(\mathcal{I}_2\), which can be written as algebraic differential operators in two variables (with polynomial coefficients) of the 2nd and 6th orders, respectively, are represented as non-linear combinations of \(g^{(2)}\) or \(g^{(3)}\) (hidden) algebra generators in a minimal manner. By using a specially designed MAPLE-18 code to deal with algebraic operators it is found that (\(H\), \(\mathcal{I}_1\), \(\mathcal{I}_2\), \(\mathcal{I}_{12} \equiv [\mathcal{I}_1, \mathcal{I}_2]\)) are the four generating elements of the \textit{quartic} polynomial algebra of integrals. This algebra is embedded into the universal enveloping algebra \(g^{(3)}\). In turn, 3-body/\(A_2\)-rational Calogero model is characterized by cubic polynomial algebra of integrals, it is mentioned briefly.
{\copyright 2024 American Institute of Physics}Diffraction by a right-angled no-contrast penetrable wedge: analytical continuation of spectral functionshttps://zbmath.org/1541.811992024-09-27T17:47:02.548271Z"Kunz, V. D."https://zbmath.org/authors/?q=ai:kunz.valentin-d"Assier, R. C."https://zbmath.org/authors/?q=ai:assier.raphael-cSummary: We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener-Hopf approach. Specifically, the analyticity properties of the unknown (spectral) functions of the two-complex-variable Wiener-Hopf equation are studied. We show that these spectral functions can be analytically continued onto a two-complex dimensional manifold, and unveil their singularities in \(\mathbb{C}^2\). To do so, integral representation formulae for the spectral functions are given and thoroughly used. It is shown that the novel concept of additive crossing holds for the penetrable wedge diffraction problem, and that we can reformulate the physical diffraction problem as a functional problem using this concept.Resummation of threshold logarithms in deeply-virtual Compton scatteringhttps://zbmath.org/1541.812002024-09-27T17:47:02.548271Z"Schoenleber, J."https://zbmath.org/authors/?q=ai:schoenleber.jSummary: I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to \(\frac{\alpha_s^n}{x\pm\xi}\log(\frac{\xi\pm x}{2\xi})^k\) in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the \(x\rightarrow\pm\xi\) limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that the corrections due to resummation for the quark contribution might be small.Classical and quantum elliptical billiards: mixed phase space and short-range correlations in singlets and doubletshttps://zbmath.org/1541.812012024-09-27T17:47:02.548271Z"Araújo Lima, T."https://zbmath.org/authors/?q=ai:araujo-lima.t"do Carmo, R. B."https://zbmath.org/authors/?q=ai:do-carmo.r-bSummary: Billiards are flat cavities where a particle is free to move between elastic collisions with the boundary. In chaos theory, these systems are simple prototypes. The conservative dynamics of a billiard may vary from regular to chaotic, depending only on the shape of the boundary. This work aims to shed light into the quantization of classically chaotic systems. We present numerical results on classical and quantum properties in two bi-parametric families of billiards, namely Elliptical Stadium Billiard (ESB) and Elliptical-\(C_3\) Billiards (E-\(C_3\)B). Both families entail elliptical perturbations of chaotic billiards with originally circular sectors on their borders. Our numerical calculations provide evidence that these elliptical families may exhibit a mixed classical dynamics, identified by the chaotic fraction of the phase space, the parameter \(\chi_{\mathrm{c}} < 1\). We use this quantity to guide our analysis of quantum spectra. We explore the short-range correlations through nearest neighbor spacing distribution \(p(s)\), revealing that in the mixed region of the classical phase space, \(p(s)\) is well described by the Berry-Robnik-Brody (BRB) distributions for the ESB. In agreement with the expectation from the so-called ergodic parameter \(\alpha = t_{\mathrm{H}}/t_{\mathrm{T}}\), the ratio between the Heisenberg time and the classical diffusive-like transport time. Our findings indicate the possibility of quantum dynamical localization when \(\alpha < 1\). For the E-\(C_3\)B family, the eigenstates can be split into singlets and doublets. BRB successfully describes \(p(s)\) for singlets as the previous family in the mixed region. However, for doublets, new distributions recently introduced in the literature come into play, providing descriptions for \(p(s)\) with a focus on cases where \(\chi_{\mathrm{c}} = 1\). We observed that as \(\chi_{\mathrm{c}}\) decreases, the \(p(s)\) distributions simultaneously deviate from the Gaussian Orthogonal Ensemble (GOE) for singlets, and Gaussian Unitary Ensemble (GUE) for doublets.A proposal for a new kind of spontaneous collapse modelhttps://zbmath.org/1541.812022024-09-27T17:47:02.548271Z"Piccione, Nicolò"https://zbmath.org/authors/?q=ai:piccione.nicoloSummary: Spontaneous collapse models are modifications of standard quantum mechanics in which a physical mechanism is responsible for the collapse of the wavefunction, thus providing a way to solve the so-called ``measurement problem''. The two most famous of these models are the Ghirardi-Rimini-Weber (GRW) model and the Continuous Spontaneous Localisation (CSL) models. Here, we propose a new kind of non-relativistic spontaneous collapse model based on the idea of collapse points situated at fixed spacetime coordinates. This model shares properties of both GRW and CSL models, while starting from different assumptions. We show that it can lead to a dynamics quite similar to that of the GRW model while also naturally solving the problem of indistinguishable particles. On the other hand, we can also obtain the same master equation of the CSL models. Then, we show how our proposed model solves the measurement problem in a manner conceptually similar to the GRW model. Finally, we show how the proposed model can also accommodate for Newtonian gravity by treating the collapses as gravitational sources.Beam functions for \(N\)-jettiness at \(\mathrm{N^3LO}\) in perturbative QCDhttps://zbmath.org/1541.812032024-09-27T17:47:02.548271Z"Baranowski, Daniel"https://zbmath.org/authors/?q=ai:baranowski.daniel"Behring, Arnd"https://zbmath.org/authors/?q=ai:behring.arnd"Melnikov, Kirill"https://zbmath.org/authors/?q=ai:melnikov.kirill"Tancredi, Lorenzo"https://zbmath.org/authors/?q=ai:tancredi.lorenzo"Wever, Christopher"https://zbmath.org/authors/?q=ai:wever.christopherSummary: We present a calculation of all matching coefficients for \(N\)-jettiness beam functions at next-to-next-to-next-to-leading order (\(\mathrm{N^3LO}\)) in perturbative quantum chromodynamics (QCD). Our computation is performed starting from the respective collinear splitting kernels, which we integrate using the axial gauge. We use reverse unitarity to map the relevant phase-space integrals to loop integrals, which allows us to employ multi-loop techniques including integration-by-parts identities and differential equations. We find a canonical basis and use an algorithm to establish non-trivial partial fraction relations among the resulting master integrals, which allows us to reduce their number substantially. By use of regularity conditions, we express all necessary boundary constants in terms of an independent set, which we compute by direct integration of the corresponding integrals in the soft limit. In this way, we provide an entirely independent calculation of the matching coefficients which were previously computed in [\textit{M. A. Ebert} et al., J. High Energy Phys. 2020, No. 9, Paper No. 143, 22 p. (2020; \url{doi:10.1007/JHEP09(2020)143})].Hall droplet sheets in holographic QCDhttps://zbmath.org/1541.812042024-09-27T17:47:02.548271Z"Bigazzi, Francesco"https://zbmath.org/authors/?q=ai:bigazzi.francesco"Cotrone, Aldo L."https://zbmath.org/authors/?q=ai:cotrone.aldo-l"Olzi, Andrea"https://zbmath.org/authors/?q=ai:olzi.andreaSummary: In single-flavor QCD, the low energy description of baryons as Skyrmions is not available. In this case, it has been proposed by Komargodski that baryons can be viewed as kinds of charged quantum Hall droplets, or ``sheets''. In this paper we propose a string theory description of the sheets in single-flavor holographic QCD, focusing on the Witten-Sakai-Sugimoto model. The sheets have a ``hard'' gluonic core, described by D6-branes, and a ``soft'' mesonic shell, dual to non-trivial D8-brane gauge field configurations. We first provide the description of an infinitely extended sheet with massless or moderately massive quarks. Then, we construct a semi-infinite sheet ending on a one-dimensional boundary, a ``vortex string''. The holographic description allows for the precise calculation of sheet observables. In particular, we compute the tension and thickness of the sheet and the vortex string, and provide their four dimensional effective actions.1-form symmetry versus large \(N\) QCDhttps://zbmath.org/1541.812052024-09-27T17:47:02.548271Z"Cherman, Aleksey"https://zbmath.org/authors/?q=ai:cherman.aleksey"Jacobson, Theodore"https://zbmath.org/authors/?q=ai:jacobson.theodore-n"Neuzil, Maria"https://zbmath.org/authors/?q=ai:neuzil.mariaSummary: We show that large \(N\) QCD does not have an emergent \(\mathbb{Z}_N\) 1-form symmetry. Our results suggest that a symmetry-based understanding of (approximate) confinement in QCD would require some further generalization of the notion of generalized global symmetries.Hot and dense QCD shear viscosity at leading loghttps://zbmath.org/1541.812062024-09-27T17:47:02.548271Z"Danhoni, Isabella"https://zbmath.org/authors/?q=ai:danhoni.isabella"Moore, Guy D."https://zbmath.org/authors/?q=ai:moore.guy-dSummary: The leading-order weak-coupling shear viscosity of QCD was computed almost 20 years ago, and the extension to next-to-leading order is 4 years old. But these results have never been applied at finite baryon chemical potential \(\mu\), despite the fact that intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here we extend the leading-log shear viscosity calculation to finite \(\mu\), and we argue that the convergence of the weak-coupling expansion, while questionable for achievable plasmas, should be better at \(\mu > T\) than at \(\mu = 0\).Infrared phases of \(2d\) QCDhttps://zbmath.org/1541.812072024-09-27T17:47:02.548271Z"Delmastro, Diego"https://zbmath.org/authors/?q=ai:delmastro.diego"Gomis, Jaume"https://zbmath.org/authors/?q=ai:gomis.jaume"Yu, Matthew"https://zbmath.org/authors/?q=ai:yu.matthewSummary: We derive the necessary and sufficient conditions for a \(2d\) QCD theory of massless gluons and left and right chiral quarks in arbitrary representations of a gauge group \(G\) to develop a mass gap. These results are obtained from spectral properties of the lightcone and temporal QCD Hamiltonians. The conditions can be explicitly solved, and we provide the complete list of all \(2d\) QCD theories that have a quantum mechanical gap in the spectrum, while any other theory not in the list is gapless. The list of gapped theories includes QCD models with quarks in vector-like as well as chiral representations. The gapped theories consist of several infinite families of classical gauge groups with quarks in rank 1 and 2 representations, plus a finite number of isolated cases. We also put forward and analyze the effective infrared description of QCD -- TQFTs for gapped theories and CFTs for gapless theories -- and exhibit several interesting features in the infrared, such as the existence of non-trivial global 't Hooft anomalies and emergent supersymmetry. We identify \(2d\) QCD theories that flow in the infrared to celebrated CFTs such as minimal models, bosonic and supersymmetric, and Wess-Zumino-Witten and Kazama-Suzuki models.Two-loop QCD corrections to the \(V\rightarrow q\bar{q}g\) helicity amplitudes with axial-vector couplingshttps://zbmath.org/1541.812082024-09-27T17:47:02.548271Z"Gehrmann, Thomas"https://zbmath.org/authors/?q=ai:gehrmann.thomas"Peraro, Tiziano"https://zbmath.org/authors/?q=ai:peraro.tiziano"Tancredi, Lorenzo"https://zbmath.org/authors/?q=ai:tancredi.lorenzoSummary: We compute the two-loop corrections to the helicity amplitudes for the coupling of a massive vector boson to a massless quark-antiquark pair and a gluon, accounting for vector and axial-vector couplings of the vector boson and distinguishing isospin non-singlet and singlet contributions. A new four-dimensional basis for the decomposition of the amplitudes into 12 invariant tensor structures is introduced. The associated form factors are then computed up to two loops in QCD using dimensional regularization. After performing renormalization and infrared subtraction, the finite parts of the renormalized non-singlet vector and axial-vector form factors are shown agree with each other, and to reproduce the previously known two-loop amplitudes. The singlet axial-vector amplitude receives a contribution from the axial anomaly from two loops onwards. This amplitude is computed for massless and massive internal quarks. Our results provide the last missing two-loop amplitudes entering the NNLO QCD corrections of vector-boson-plus-jet production at hadron colliders.Configurational Entropy and the \(\mathcal{N}^\ast(1440)\) Roper resonance in QCDhttps://zbmath.org/1541.812092024-09-27T17:47:02.548271Z"Karapetyan, G."https://zbmath.org/authors/?q=ai:karapetyan.garnik-a|karapetyan.gevork-yaSummary: The electroexcitation of the \(\mathcal{N}^\ast(1440)\) Roper resonance, which defines the first radially excited state of the nucleon, is examined within the soft-wall AdS/QCD model. Such excited Fock states are characterized by the leading three-quark component, which determines the main properties of Roper resonance. The differential configurational entropy (DCE) was used in the nuclear interaction with a gauge vector field for \(\mathcal{N}^\ast(1440)\) transition. Comparing the main results with the recent data of the CLAS Collaboration at JLab shows a good agreement on the accuracy of the computed data.Constraints on the hadronic light-by-light in the Melnikov-Vainshtein regimehttps://zbmath.org/1541.812102024-09-27T17:47:02.548271Z"Bijnens, Johan"https://zbmath.org/authors/?q=ai:bijnens.johan"Hermansson-Truedsson, Nils"https://zbmath.org/authors/?q=ai:truedsson.nils-hermansson"Rodríguez-Sánchez, Antonio"https://zbmath.org/authors/?q=ai:rodriguez-sanchez.antonioSummary: The muon anomalous magnetic moment continues to attract attention due to the possible tension between the experimentally measured value and the theoretical Standard Model prediction. With the aim to reduce the uncertainty on the hadronic light-by-light contribution to the magnetic moment, we derive short-distance constraints in the Melnikov-Vainshtein regime which are useful for data-driven determinations. In this kinematical region, two of the four electromagnetic currents are close in the four-point function defining the hadronic light-by-light tensor. To obtain the constraints, we develop a systematic operator product expansion of the tensor in question to next-to-leading order in the expansion in operators. We evaluate the leading in \(\alpha_s\) contributions and derive constraints for the next-to-leading operators that are also valid nonperturbatively.Polarisability and magnetisation of electrically \(K\)-mouflaged objects: the Born-Infeld modmax case studyhttps://zbmath.org/1541.812112024-09-27T17:47:02.548271Z"Jiménez, Jose Beltrán"https://zbmath.org/authors/?q=ai:jimenez.jose-beltran"Bettoni, Dario"https://zbmath.org/authors/?q=ai:bettoni.dario"Brax, Philippe"https://zbmath.org/authors/?q=ai:brax.philippeSummary: We consider a family of non-linear theories of electromagnetism that interpolate between Born-Infeld at small distances and the recently introduced ModMax at large distances. These models are duality invariant and feature a \(K\)-mouflage screening in the Born-Infeld regime. We focus on computing the static perturbations around a point-like screened charge in terms of two decoupled scalar potentials describing the polar and the axial sectors respectively. Duality invariance imposes that the propagation speed of the odd perturbations goes to zero as fast as the effective screened charge of the object, potentially leading to strong coupling and an obstruction to the viability of the EFT below the screened radius. We then consider the linear response to external fields and compute the electric polarisability and the magnetic susceptibility. Imposing regularity of the perturbations at the position of the particle, we find that the polarisability for the odd multipoles vanishes whilst for the magnetisation Born-Infeld emerges as the only theory with vanishing susceptibility for even multipoles. The perturbation equations factorise in terms of ladder operators connecting different multipoles. There are two such ladder structures for the even sector: one that acts as an automorphism between the first four multipoles and another one that connects multipoles separated by four units. When requiring a similar ladder structure for the odd sector, Born-Infeld arises again as the unique theory. We use this ladder structure to relate the vanishing of the polarisability and the susceptibility to the values of conserved charges. Finally the perturbation equations correspond to a supersymmetric quantum mechanical system such that the polar sector can be described in terms of Schrödinger's equations with four generalised hyperbolic Pösch-Teller potentials whose eigenfunctions are in correspondence with the multipoles.Charge asymmetry in the spectra of Bremsstrahlung and pair productionhttps://zbmath.org/1541.812122024-09-27T17:47:02.548271Z"Krachkov, Petr A."https://zbmath.org/authors/?q=ai:krachkov.petr-a"Lee, Roman N."https://zbmath.org/authors/?q=ai:lee.roman-nSummary: We calculate the first Coulomb correction to the spectra of two processes: the electron bremsstrahlung and electron-positron photoproduction in the Coulomb field. We show that, in contrast to the results obtained in the Born approximation and in the high-energy limit, the obtained corrections for these two process are not related by the crossing symmetry substitutions. The found corrections determine the leading contribution to the charge asymmetry in these processes. We use modern multiloop methods based on the IBP reduction and on the differential equations for master integrals. The results are presented in terms of classical polylogarithms. We provide both the threshold and the high-energy asymptotics of the obtained expressions and compare them with available results.Lepton flavor violating decays \(l_j\rightarrow l_i\gamma\gamma\)https://zbmath.org/1541.812132024-09-27T17:47:02.548271Z"Liu, Ming-Yue"https://zbmath.org/authors/?q=ai:liu.mingyue"Zhao, Shu-Min"https://zbmath.org/authors/?q=ai:zhao.shumin"Wang, Yi-Tong"https://zbmath.org/authors/?q=ai:wang.yitong"Wang, Xi"https://zbmath.org/authors/?q=ai:wang.xi.2|wang.xi"Long, Xin-Xin"https://zbmath.org/authors/?q=ai:long.xin-xin"Wang, Tong-Tong"https://zbmath.org/authors/?q=ai:wang.tongtong"Zhang, Hai-Bin"https://zbmath.org/authors/?q=ai:zhang.haibin"Feng, Tai-Fu"https://zbmath.org/authors/?q=ai:feng.tai-fuSummary: In this paper, we study the lepton flavor violating decays of the \(l_j \to l_i\gamma\gamma\) (\(j=2, 3\); \(i=1, 2\)) processes under the \(U(1)_X\)SSM. The \(U(1)_X\)SSM is the addition of three singlet new Higgs superfields and right-handed neutrinos to the minimal supersymmetric standard model (MSSM). Based on the latest experimental constraints of \(l_j\to l_i\gamma\gamma\), we analyze the effects of different sensitive parameters on the results and made reasonable predictions for future experimental development. Numerical analysis shows that many parameters have a greater or lesser effect on lepton flavor violation (LFV), but the main sensitive parameters and sources leading to LFV are the non-diagonal elements involving the initial and final leptons. This work could provide a basis for the discovery of the existence of new physics (NP).Embedding of the Georgi-Glashow SU(5) model in the superconformal algebrahttps://zbmath.org/1541.812142024-09-27T17:47:02.548271Z"Alvarez, P. D."https://zbmath.org/authors/?q=ai:alvarez.pedro-d"Chavez, R. A."https://zbmath.org/authors/?q=ai:chavez.r-a"Zanelli, J."https://zbmath.org/authors/?q=ai:zanelli.jorgeSummary: We present a scheme to construct grand unified models based on the superconformal algebra and the inclusion of matter fields in the adjoint representation of supersymmetry. As an illustration, we implemented the Georgi-Glashow SU(5) model. The model predicts the existence of a dark \((\mathbf{1}, \mathbf{24}, 0) + (\mathbf{5}, \mathbf{5^\ast}, -y^\prime) + (\mathbf{5^\ast}, \mathbf{5}, y^\prime)\) sector and an anomalous \(\mathrm{U}(1)_Z\).3HDM with \(\Delta(27)\) symmetry and its phenomenological consequenceshttps://zbmath.org/1541.812152024-09-27T17:47:02.548271Z"Kalinowski, J."https://zbmath.org/authors/?q=ai:kalinowski.jan"Kotlarski, W."https://zbmath.org/authors/?q=ai:kotlarski.wojciech"Rebelo, M. N."https://zbmath.org/authors/?q=ai:rebelo.m-n"de Medeiros Varzielas, I."https://zbmath.org/authors/?q=ai:varzielas.i-de-medeiros|de-medeiros-varzielas.ivoSummary: We perform a comprehensive analysis of a version of the 3-Higgs doublet model whose scalar potential is invariant under a global \(\Delta(27)\) discrete symmetry and where the three scalar doublets are chosen to transform as a triplet under this discrete group. For each of the known tree-level minima we study the mass spectra and use the oblique parameters \textit{STU} as well as perturbative unitarity to constrain the parameter space of the model. We then discuss phenomenological consequences of some leading order flavour mixing quark Yukawa couplings by considering the flavour violation process \(b\rightarrow s\gamma\).
We show that perturbative unitarity significantly constrains parameters of the model while, conversely, the beyond the Standard Model contributions to the \(b\rightarrow s\gamma\) decay are automatically tamed by the symmetry.Self-dual solutions of a field theory model of two linked ringshttps://zbmath.org/1541.812162024-09-27T17:47:02.548271Z"Taklimi, Neda Abbasi"https://zbmath.org/authors/?q=ai:taklimi.neda-abbasi"Ferrari, Franco"https://zbmath.org/authors/?q=ai:ferrari.franco"Piątek, Marcin R."https://zbmath.org/authors/?q=ai:piatek.marcin-rSummary: In this work the connection established in [\textit{F. Ferrari}, Phys. Lett., A 323, No. 5--6, 351--359 (2004; Zbl 1118.81346); \textit{F. Ferrari} et al., Nucl. Phys., B 945, Article ID 114673, 35 p. (2019; Zbl 1430.82016)] between a model of two linked polymers rings with fixed Gaussian linking number forming a 4-plat and the statistical mechanics of non-relativistic anyon particles is explored. The excluded volume interactions have been switched off and only the interactions of entropic origin arising from the topological constraints are considered. An interpretation from the polymer point of view of the field equations that minimize the energy of the model in the limit in which one of the spatial dimensions of the 4-plat becomes very large is provided. It is shown that the self-dual contributions are responsible for the long-range interactions that are necessary for preserving the global topological properties of the system during the thermal fluctuations. The non self-dual part is also related to the topological constraints, and takes into account the local interactions acting on the monomers in order to prevent the breaking of the polymer lines. It turns out that the energy landscape of the two linked rings is quite complex. Assuming as a rough approximation that the monomer densities of half of the 4-plat are constant, at least two points of energy minimum are found. Classes of non-trivial self-dual solutions of the self-dual field equations are derived. One of these classes is characterized by densities of monomers that are the squared modulus of holomorphic functions. The second class is obtained under some assumptions that allow to reduce the self-dual equations to an analog of the Gouy-Chapman equation for the charge distribution of ions in a double layer capacitor. In the present case, the spatial distribution of the electric potential of the ions is replaced by the spatial distribution of the fictitious magnetic fields associated with the presence of the topological constraints. In the limit in which two of the spatial dimensions are large in comparison with the third one, we provide exact formulas for the conformations of the monomer densities of the 4-plat by using the elliptic, hyperbolic and trigonometric solutions of the sinh-Gordon and cosh-Gordon equations which have been used for instance in the construction of classical string solutions in AdS3 and dS3 [\textit{I. Bakas} and \textit{G. Pastras}, J. High Energy Phys. 2016, No. 7, Paper No. 70, 53 p. (2016; Zbl 1390.81407)].Local spatial densities for composite Spin-3/2 systemshttps://zbmath.org/1541.812172024-09-27T17:47:02.548271Z"Alharazin, H."https://zbmath.org/authors/?q=ai:alharazin.h"Sun, B.-D."https://zbmath.org/authors/?q=ai:sun.bangdong"Epelbaum, E."https://zbmath.org/authors/?q=ai:epelbaum.evgeny"Gegelia, J."https://zbmath.org/authors/?q=ai:gegelia.jambul"Meißner, U.-G."https://zbmath.org/authors/?q=ai:meissner.ulf-gSummary: The definition of local spatial densities by using sharply localized one-particle states is applied to spin-3/2 systems. Matrix elements of the electromagnetic current and the energy-momentum tensor are considered and integral expressions of associated spatial distributions in terms of form factors are derived.Heavy axions from twin dark sectors with \(\bar{\theta}\)-characterized mirror symmetryhttps://zbmath.org/1541.812182024-09-27T17:47:02.548271Z"Gu, Pei-Hong"https://zbmath.org/authors/?q=ai:gu.pei-hongSummary: The QCD Lagrangian contains a CP violating gluon density term with a physical coefficient \(\bar{\theta}\). The upper bound on the electric dipole moment of neutron requires the value of \(\bar{\theta}\) to be extremely small. The tiny \(\bar{\theta}\) is commonly known as the strong CP problem. In order to solve this puzzle, we construct a \(\bar{\theta}\)-characterized mirror symmetry between a pair of twin dark sectors with respective discrete symmetries. By taking a proper phase rotation of dark fields, we can perfectly remove the parameter \(\bar{\theta}\) from the full Lagrangian. In our scenario, the discrete symmetry breaking, which are responsible for the mass generation of dark colored fermions and dark matter fermions, can be allowed near the TeV scale. This means different phenomena from the popular axion models with high scale Peccei-Quinn global symmetry breaking.Elementary coupling coefficients for the Wigner supermultiplet symmetryhttps://zbmath.org/1541.812192024-09-27T17:47:02.548271Z"Pan, Feng"https://zbmath.org/authors/?q=ai:pan.feng"Dai, Lianrong"https://zbmath.org/authors/?q=ai:dai.lianrong"Draayer, Jerry P."https://zbmath.org/authors/?q=ai:draayer.jerry-pSummary: An algorithm for evaluating Wigner coefficients of \(\mathrm{U}(4)\supset\mathrm{SU}_S(2)\otimes\mathrm{SU}_T(2)\) for the coupling \([n_{14}, n_{24}, n_{34}, n_{44}] \otimes [1, 0, 0, 0] \downarrow [m_{14}, m_{24}, m_{34}, m_{44}]\) with arbitrary irreducible representation \([n_{14}, n_{24}, n_{34}, n_{44}]\) is provided based on the algebraic expressions with the expansion coefficients of the \(\mathrm{U}(4)\supset\mathrm{SU}_S(2)\otimes\mathrm{SU}_T(2)\) states in terms of those in the U(4) canonical basis and the Clebsch-Gordan coefficients of U(4) in the canonical basis. The state expansion coefficients are evaluated as the components of the null space vectors of the spin-isospin projection matrices.An alternative approach to normalizing the Coulomb \(R_{n\ell}(r)\) radial solutionshttps://zbmath.org/1541.812202024-09-27T17:47:02.548271Z"Reed, B. Cameron"https://zbmath.org/authors/?q=ai:reed.bruce-cameron"Bason, Gregory L."https://zbmath.org/authors/?q=ai:bason.gregory-lSummary: The normalization of the radial functions \(R_{n\ell}(r)\) for the solution of Schrödinger's equation for the Coulomb potential usually proceeds by appealing to the properties of Associated Laguerre polynomials. In this paper we show how to effect the normalization directly from the overall form of the solution and the recursion relation for its series part. Our approach should be applicable to similar problems, such as the harmonic oscillator, and can serve to offer students an alternate method of establishing fully-normalized wavefunctions without invoking the properties of special functions.Cyclification of orbifoldshttps://zbmath.org/1541.812212024-09-27T17:47:02.548271Z"Sati, Hisham"https://zbmath.org/authors/?q=ai:sati.hisham"Schreiber, Urs"https://zbmath.org/authors/?q=ai:schreiber.ursSummary: Inertia orbifolds homotopy-quotiented by rotation of \textit{geometric} loops play a fundamental role not only in ordinary cyclic cohomology, but more recently in constructions of equivariant Tate-elliptic cohomology and generally of transchromatic characters on generalized cohomology theories. Nevertheless, existing discussion of such \textit{cyclified stacks} has been relying on ad-hoc component presentations with intransparent and unverified stacky homotopy type. Following our previous formulation of transgression of cohomological charges (``double-dimensional reduction''), we explain how cyclification of \(\infty\)-stacks is a fundamental and elementary base-change construction over moduli stacks in cohesive higher topos theory (cohesive homotopy-type theory). We prove that Ganter/Huan's extended inertia groupoid used to define equivariant quasi-elliptic cohomology is indeed a model for this intrinsically defined cyclification of orbifolds, and we show that cyclification implements transgression in group cohomology in general, and hence in particular the transgression of degree-4 twists of equivariant Tate-elliptic cohomology to degree-3 twists of orbifold \(K\)-theory on the cyclified orbifold. As an application, we show that the universal shifted integral 4-class of equivariant 4-Cohomotopy theory on ADE-orbifolds induces the Platonic 4-twist of ADE-equivariant Tate-elliptic cohomology, and we close by explaining how this should relate to elliptic M5-brane genera, under our previously formulated \textit{Hypothesis H}.Spectral approximation scheme for a hybrid, spin-density Kohn-Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energyhttps://zbmath.org/1541.812222024-09-27T17:47:02.548271Z"Melgaard, M."https://zbmath.org/authors/?q=ai:melgaard.michael|melgard.m"Syrjanen, V. J. J."https://zbmath.org/authors/?q=ai:syrjanen.v-j-jSummary: We provide a mathematical justification of a spectral approximation scheme known as spectral binning for the Kohn-Sham spin density-functional theory in the presence of an external (nonuniform) magnetic field and a collinear exchange-correlation energy term. We use an extended density-only formulation for modeling the magnetic system. No current densities enter the description in this formulation, but the particle density is split into different spin components. By restricting the exchange-correlation energy functional to be of a collinear LSDA form, we prove a series of results which enable us to mathematically justify the spectral binning scheme using the method of Gamma-convergence, in conjunction with auxiliary steps involving recasting the electrostatic potentials, justifying the spectral approximation by making a spectral decomposition of the Hamiltonian and ``linearizing'' the latter Hamiltonian.Quantifying the distortion by spin-orbit and spin-spin coupling in molecular clusters using molecular quantum similarityhttps://zbmath.org/1541.812232024-09-27T17:47:02.548271Z"Morales-Bayuelo, Alejandro"https://zbmath.org/authors/?q=ai:morales-bayuelo.alejandroSummary: The manuscript discusses the concepts of spin-orbit and spin-spin coupling in atomic physics and Molecular Quantum Similarity (MQS) in molecular clusters. spin-orbit and spin-spin coupling arises from the interaction between an electron's spin and its motion around the nucleus and electron-electron interaction and plays a crucial role in determining energy levels and spectral lines in atoms with heavy nuclei. On the other hand, MQS is a computational approach to compare the electronic density distributions in different molecular systems. In this order of ideas, the study aims to answer questions about electronic and structural differences caused by the spin-orbit and spin-spin coupling from the initial geometry [Steradians (SR) geometry] using the MQS framework. The MQS is based on the Molecular Quantum Similarity Measure (MQSM) using different positive operators such as Dirac delta and Coulomb operators to quantify the similarity between molecular systems. The paper presents tables with MQSM indices and Euclidean distances for different molecular clusters using initial geometry vs. geometry involved spin-orbit and spin-spin coupling. The scalar, spin-orbit and spin-spin relativistic coupling were incorporated using Amsterdam Density Functional code. The results show significant coupling of spin-orbit and spin-spin coupling on the similarity measures between different molecules. The manuscript suggests that understanding the relationship between spin-orbit and spin-spin coupling and quantum similarity could lead to deeper insights into electronic interactions in complex molecular systems and has potential applications in quantum mechanics and molecular physics.Fractional Hall conductivity and spin-c structure in solvable lattice Hamiltonianshttps://zbmath.org/1541.812242024-09-27T17:47:02.548271Z"Han, Zhaoyu"https://zbmath.org/authors/?q=ai:han.zhaoyu"Chen, Jing-Yuan"https://zbmath.org/authors/?q=ai:chen.jingyuanSummary: The Kapustin-Fidkowski no-go theorem forbids U(1) symmetric topological orders with non-trivial Hall conductivity in (2+1)d from admitting commuting projector Hamiltonians, where the latter is the paradigmatic method to construct exactly solvable lattice models for topological orders. Even if a topological order would intrinsically have admitted commuting projector Hamiltonians, the theorem forbids so once its interplay with U(1) global symmetry which generates Hall conductivity is taken into consideration. Nonetheless, in this work, we show that for all (2+1)d U(1) symmetric abelian topological orders of such kind, we can construct a lattice Hamiltonian that is controllably solvable at low energies, even though not ``exactly'' solvable; hence, this no-go theorem does not lead to significant difficulty in the lattice study of these topological orders. Moreover, for the fermionic topological orders in our construction, we introduce the lattice notion of spin-c structure --- a concept important in the continuum that has previously not been adequately introduced in the lattice context.Infinite critical Boson induced non-Fermi liquid in \(d = 3 - \epsilon\) dimensionshttps://zbmath.org/1541.812252024-09-27T17:47:02.548271Z"Pan, Zhiming"https://zbmath.org/authors/?q=ai:pan.zhiming"Zhang, Xiao-Tian"https://zbmath.org/authors/?q=ai:zhang.xiaotianSummary: We study the fermion-boson coupled system in \(d = 3 - \epsilon\) space dimensions near the quantum phase transition; infinite many boson modes locating on a sphere become critical simultaneously, which is dubbed ``critical boson surface'' (CBS). The fermions on the Fermi surface can be scattered to nearby points locating on a boson ring in the low-energy limit. The large number of the boson scattering channels \(N\) renders the well-known Landau damping effect largely suppressed. We propose an effective theory for a single point on the Fermi surface and the associated critical boson ring induced by the boson scattering channels. Based on the effective model, one-loop renormalization group analysis is performed with asymptotic \(\epsilon\)-expansion. The fermion self-energy and Yukawa interaction vertex are dressed with \(\epsilon\) poles and are largely enhanced due to the presence of critical boson ring. The imaginary part of the self-energy exhibits a linear-in frequency dependence and the real part gives a vanishing quasiparticle weight in the low-energy limit, which signatures the celebrated ``marginal Fermi liquid'' behavior. We find a novel non-Fermi liquid fixed point, at which the critical properties show features associated with the CBS.Trace and diffeomorphism anomalies of the classical Liouville theory, Virasoro algebras, Weyl-gauging and all thathttps://zbmath.org/1541.812262024-09-27T17:47:02.548271Z"Haman, Pavel"https://zbmath.org/authors/?q=ai:haman.pavel"Iorio, Alfredo"https://zbmath.org/authors/?q=ai:iorio.alfredoSummary: To fully clarify the invariance of the classical Liouville field theory under the Virasoro algebra, we first elucidate in detail the concept of \textit{classical anomaly}, discuss the occurrence of two symmetry algebras associated to this theory, and provide some new formulae to compute the classical center in a general fashion. We apply this to the study of the symmetries of the free boson in two dimensions. Moving to Liouville, we see how this gives rise to an energy-momentum tensor with non-tensorial conformal transformations, in flat space, and a non-vanishing trace, in curved space. We provide a variety of improvements of the (local) theory, that restore Weyl invariance. With explicit computations, we show that the covariant conservation of the Weyl-invariance-improved energy-momentum tensor is lost, in general, and relate the chosen improvement with the corresponding subset of preserved diffeomorphisms. The non-tensorial transformation rule of the Weyl-invariance-improved energy-momentum tensor in curved space is explicitly back-traced to the Virasoro center.Effect of the three-body interactions on the reduction of the exchange dipolar termhttps://zbmath.org/1541.812272024-09-27T17:47:02.548271Z"Kouidri, Smain"https://zbmath.org/authors/?q=ai:kouidri.smainSummary: We focus our study on the effect of the exchange dipolar term in the absence/presence of three-body interactions for the Bose dipolar gas using two approximations firstly that of Hartree-Fock-Bogoliubov Popov (HFB-P) where the anomalous density is totally neglected and secondly the generalized Hartree-Fock-Bogoliubov (GHFB) approximation which takes it into account. The aim is to determine the three densities: the condensed density, the non-condensed density and the anomalous density \textit{via} different aspect ratios. The analyze of the comportment of the exchange dipolar term as a function of \(\frac{T}{T_c}\) and the role of the effect of three-body interactions played in the treatment of this physical quantity and more particularly the collective excitation modes take place in this work.3-manifolds and VOA charactershttps://zbmath.org/1541.812282024-09-27T17:47:02.548271Z"Cheng, Miranda C. N."https://zbmath.org/authors/?q=ai:cheng.miranda-c-n"Chun, Sungbong"https://zbmath.org/authors/?q=ai:chun.sungbong"Feigin, Boris"https://zbmath.org/authors/?q=ai:feigin.boris-l"Ferrari, Francesca"https://zbmath.org/authors/?q=ai:ferrari.francesca"Gukov, Sergei"https://zbmath.org/authors/?q=ai:gukov.sergei"Harrison, Sarah M."https://zbmath.org/authors/?q=ai:harrison.sarah-m"Passaro, Davide"https://zbmath.org/authors/?q=ai:passaro.davideSummary: By studying the properties of \(q\)-series \(\widehat{Z}\)-invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for \(\widehat{Z}\)-invariants leads to many infinite families of new fermionic formulae for VOA characters.Connection probabilities of multiple FK-Ising interfaceshttps://zbmath.org/1541.820022024-09-27T17:47:02.548271Z"Feng, Yu"https://zbmath.org/authors/?q=ai:feng.yu"Peltola, Eveliina"https://zbmath.org/authors/?q=ai:peltola.eveliina"Wu, Hao"https://zbmath.org/authors/?q=ai:wu.hao.2Summary: We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight \({q \in [1,4)}\). Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of \(q\) than the FK-Ising model \((q=2)\). Given the convergence of interfaces, the conjectural formulas for other values of \(q\) could be verified similarly with relatively minor technical work. The limit interfaces are variants of \(\mathrm{SLE}_\kappa\) curves (with \(\kappa = 16/3\) for \(q=2\)). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all \(q \in [1,4)\), thus providing further evidence of the expected CFT description of these models.Multicriticality in Yang-Lee edge singularityhttps://zbmath.org/1541.820042024-09-27T17:47:02.548271Z"Lencsés, Máté"https://zbmath.org/authors/?q=ai:lencses.mate"Miscioscia, Alessio"https://zbmath.org/authors/?q=ai:miscioscia.alessio"Mussardo, Giuseppe"https://zbmath.org/authors/?q=ai:mussardo.giuseppe"Takács, Gábor"https://zbmath.org/authors/?q=ai:takacs.gaborSummary: In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin \(\mathbb{Z}_2\) odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin \(\mathbb{Z}_2\) even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the conformal non-unitary minimal models \(\mathcal{M}(2, 5)\) and \(\mathcal{M}(2, 7)\) respectively, which is supported by considerations based on \(\boldsymbol{PT}\) symmetry and the corresponding extension of Zamolodchikov's \(c\)-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [\textit{G. von Gehlen}, Int. J. Mod. Phys. B 8, No. 25--26, 3507--3529 (1994; \url{doi:10.1142/S0217979294001494}), see also Zbl 0877.60087]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.A proof of finite crystallization via stratificationhttps://zbmath.org/1541.820142024-09-27T17:47:02.548271Z"Friedrich, Manuel"https://zbmath.org/authors/?q=ai:friedrich.manuel"Kreutz, Leonard"https://zbmath.org/authors/?q=ai:kreutz.leonard-cAuthors' abstract: We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle interactions and three-body angular potentials favoring bond-angles of the square lattice. To each configuration, we associate its bond graph which is then suitably modified by identifying chains of successive atoms. This method, called \textit{stratification}, reduces the crystallization problem to a simple minimization that corresponds to a proof via slicing of the isoperimetric inequality in $\ell^1$. As a byproduct, we also prove a fluctuation estimate for minimizers of the configurational energy, known as the $n^{3/4}$-law
Reviewer: Xingbin Pan (Shanghai)Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric modelshttps://zbmath.org/1541.830052024-09-27T17:47:02.548271Z"Marchetti, Luca"https://zbmath.org/authors/?q=ai:marchetti.luca"Oriti, Daniele"https://zbmath.org/authors/?q=ai:oriti.daniele"Pithis, Andreas G. A."https://zbmath.org/authors/?q=ai:pithis.andreas-g-a"Thürigen, Johannes"https://zbmath.org/authors/?q=ai:thurigen.johannesSummary: In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a coarse grained level, via a process involving a phase transition. In this work we show for the first time how phase transitions for realistic TGFT models can be realized using Landau-Ginzburg mean-field theory. More precisely, we consider models generating 4-dimensional Lorentzian triangulations formed by spacelike tetrahedra the quantum geometry of which is encoded in non-local degrees of freedom on the non-compact group \(\mathrm{SL}(2, \mathbb{C})\) and subject to gauge and simplicity constraints. Further we include \(\mathbb{R}\)-valued variables which may be interpreted as discretized scalar fields typically employed as a matter reference frame. We apply the Ginzburg criterion finding that fluctuations around the non-vanishing mean-field vacuum remain small at large correlation lengths regardless of the combinatorics of the non-local interaction validating the mean-field theory description of the phase transition. This work represents a first crucial step to understand phase transitions in compelling TGFT models for quantum gravity and paves the way for a more complete analysis via functional renormalization group techniques. Moreover, it supports the recent extraction of effective cosmological dynamics from TGFTs in the context of a mean-field approximation.Gravitational Coleman-Weinberg mechanismhttps://zbmath.org/1541.830092024-09-27T17:47:02.548271Z"Álvarez-Luna, Clara"https://zbmath.org/authors/?q=ai:alvarez-luna.clara"de la Calle-Leal, Sergio"https://zbmath.org/authors/?q=ai:de-la-calle-leal.sergio"Cembranos, José A. R."https://zbmath.org/authors/?q=ai:cembranos.jose-a-r"Sanz-Cillero, Juan José"https://zbmath.org/authors/?q=ai:sanz-cillero.juan-joseSummary: The Coleman-Weinberg mechanism provides a procedure by which a scalar field, which initially has no mass parameters, acquires a mass due to the anomalous nature of scale symmetry. Loop corrections trigger a spontaneous symmetry breaking and the appearance of a non-trivial vacuum. We first review the basic example of the Coleman-Weinberg mechanism, scalar Quantum Electrodynamics, in a perturbative regime where the scalar particle becomes massive through photon loops. We then present the main results of this article, what we name the gravitational Coleman-Weinberg mechanism: we analyse the same effect in a gravitational theory without explicit energy scales at tree-level. Finally, we also study the mechanism for two scalar fields in the mentioned gravitational theory. We will derive the gravitational Coleman-Weinberg potentials, analyse the parameter space where we have a symmetry breaking, and obtain the value of the corresponding scalar masses.No invariant perfect qubit codeshttps://zbmath.org/1541.830142024-09-27T17:47:02.548271Z"Mansuroglu, Refik"https://zbmath.org/authors/?q=ai:mansuroglu.refik"Sahlmann, Hanno"https://zbmath.org/authors/?q=ai:sahlmann.hannoSummary: Perfect tensors describe highly entangled quantum states that have attracted particular attention in the fields of quantum information theory and quantum gravity. In loop quantum gravity, the natural question arises whether SU(2) invariant tensors, which are fundamental ingredients of the basis states of spacetime, can also be perfect. In this work, we present a number of general constraints for the layout of such invariant perfect tensors (IPTs) and further describe a systematic and constructive approach to check the existence of an IPT of given valence. We apply our algorithm to show that no qubit encoding of valence 6 can be described by an IPT and close a gap to prove a no-go theorem for invariant perfect qubit encodings. We also provide two alternative proofs for the non-existence of 4-valent qubit IPTs which has been shown in [\textit{A. Higuchi} and \textit{A. Sudbery}, Phys. Lett., A 273, No. 4, 213--217 (2000; Zbl 1059.81511); \textit{Y. Li} et al., New J. Phys. 19, Article ID 063029, 15 p. (2017; \url{doi:10.1088/1367-2630/aa7235})].Entanglement-induced deviation from the geodesic motion in quantum gravityhttps://zbmath.org/1541.830152024-09-27T17:47:02.548271Z"Pipa, Francisco"https://zbmath.org/authors/?q=ai:pipa.francisco"Paunković, Nikola"https://zbmath.org/authors/?q=ai:paunkovic.nikola"Vojinović, Marko"https://zbmath.org/authors/?q=ai:vojinovic.markoSummary: We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general relativity, we introduce the similar notion of an effective equation of motion, but starting from an abstract quantum gravity description. In the presence of entanglement between gravity and matter, quantum effects give rise to modifications of the geodesic trajectory, primarily as a consequence of the interference between various coherent states of the gravity-matter system. Finally, we discuss the status of the weak equivalence principle in quantum gravity and its possible violation due to the nongeodesic motion.Scaling solutions for asymptotically free quantum gravityhttps://zbmath.org/1541.830162024-09-27T17:47:02.548271Z"Sen, Saswato"https://zbmath.org/authors/?q=ai:sen.saswato"Wetterich, Christof"https://zbmath.org/authors/?q=ai:wetterich.christof"Yamada, Masatoshi"https://zbmath.org/authors/?q=ai:yamada.masatoshiSummary: We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a renormalizable quantum field theory of gravity. If the proposed scaling solution is confirmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity.Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlationhttps://zbmath.org/1541.830182024-09-27T17:47:02.548271Z"Chen, Liangyu"https://zbmath.org/authors/?q=ai:chen.liangyu"Wang, Huajia"https://zbmath.org/authors/?q=ai:wang.huajiaSummary: Causal shadows are bulk space-time regions between the entanglement wedges and the causal wedges, their existence encodes deep aspects of the entanglement wedge reconstruction in the context of subregion duality in AdS/CFT. In this paper, we study the perturbation theory of the causal shadows and their relation to the properties of the associated modular flows. We first revisit the cases of degenerate causal shadows based on known examples, and discuss the origin for their degeneracy via the local nature of the modular flow. We then focus on the perturbative case in which the CFT subregion consists of two spheres separated by a large distance \(L \gg R_{1, 2}\). The RT surfaces still agree with the causal horizons, giving a degenerate causal shadow classically. We compute the corrections to the quantum extremal surfaces (Q.E.S) from the bulk mutual information, which then give rise to a non-degenerate causal shadow at order \(G_N\). We end by discussing the causal shadow perturbation theory more generally, in particular we explore the possibility of extracting the positivity conditions characterizing perturbative causal shadows in the boundary CFTs.Scattering amplitudes and \(N\)-body post-Minkowskian Hamiltonians in general relativity and beyondhttps://zbmath.org/1541.830192024-09-27T17:47:02.548271Z"Jones, Callum R. T."https://zbmath.org/authors/?q=ai:jones.callum-r-t"Solon, Mikhail"https://zbmath.org/authors/?q=ai:solon.mikhail-pSummary: We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for \(N\) non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for \(N > 2\) are described including the subtraction of tree-like iteration contributions and the calculation of non-trivial many-body Fourier transform integrals needed to construct position space potentials. A new approach to calculating these integrals as an expansion in the hierarchical limit is described based on the method of regions. As an explicit example, we present the \(\mathcal{O}(G^2)\) 3-body momentum space potential in general relativity as well as for charged bodies in Einstein-Maxwell. The result is shown to be in perfect agreement with previous post-Newtonian calculations in general relativity up to \(\mathcal{O}(G^2v^4)\). Furthermore, in appropriate limits the result is shown to agree perfectly with relativistic probe scattering in multi-center extremal black hole backgrounds and with the scattering of slowly-moving extremal black holes in the moduli space approximation.One-loop amplitudes in Einstein-Yang-Mills from forward limitshttps://zbmath.org/1541.830202024-09-27T17:47:02.548271Z"Porkert, Franziska"https://zbmath.org/authors/?q=ai:porkert.franziska"Schlotterer, Oliver"https://zbmath.org/authors/?q=ai:schlotterer.oliverSummary: We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as (super-)Yang-Mills with the so-called YM+\(\phi^3\) theory -- pure Yang-Mills coupled to bi-adjoint scalars -- which we implement via one-loop Cachazo-He-Yuan formulae. The YM+\(\phi^3\) building blocks are obtained from forward limits of tree-level input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings \(g\) and \(\kappa\). On the one hand, we spell out supersymmetry- and dimension-agnostic relations that reduce loop integrands of Einstein-Yang-Mills to those of pure gauge theories. On the other hand, we present four-point results for maximal and half-maximal supersymmetry where all supersymmetry cancellations are exposed. In the half-maximal case, we determine six-dimensional anomalies due to chiral hypermultiplets in the loop.Holographic collisions in large \(D\) effective theoryhttps://zbmath.org/1541.830252024-09-27T17:47:02.548271Z"Luna, Raimon"https://zbmath.org/authors/?q=ai:luna.raimon"Sanchez-Garitaonandia, Mikel"https://zbmath.org/authors/?q=ai:sanchez-garitaonandia.mikelSummary: We study collisions of Gaussian mass-density blobs in a holographic plasma, using a large \(D\) effective theory, as a model for holographic shockwave collisions. The simplicity of the effective theory allows us to perform the first \(4+1\) collisions in Einstein-Maxwell theory, which are dual to collisions of matter with non-zero baryonic number. We explore several collision scenarios with different blob shapes, impact parameters and charge values and find that collisions with impact parameter below the transverse width of the blobs are equivalent under rescaling. We also observe that charge weakly affects the rest of quantities. Finally, we study the entropy generated during collisions, both by charge diffusion and viscous dissipation. Multiple stages of linear entropy growth are identified, whose rates are not independent of the initial conditions.Bound states of pseudo-Dirac dark matterhttps://zbmath.org/1541.830282024-09-27T17:47:02.548271Z"Bhattacharya, Arindam"https://zbmath.org/authors/?q=ai:bhattacharya.arindam"Slatyer, Tracy R."https://zbmath.org/authors/?q=ai:slatyer.tracy-rSummary: We study the bound-state spectrum in a simple model of pseudo-Dirac dark matter, and examine how the rate of bound-state formation through radiative capture compares to Sommerfeld-enhanced annihilation. We use this model as an example to delineate the new features induced by the presence of a mass splitting between the dark matter and a nearly-degenerate partner, compared to the case where only a single dark-matter-like state is present. We provide a simple analytic prescription for estimating the spectrum of bound states in systems containing a mass splitting, which in turn allows characterization of the resonances due to near-zero-energy bound states, and validate this estimate both for pseudo-Dirac dark matter and for the more complex case of wino dark matter. We demonstrate that for pseudo-Dirac dark matter the capture rate into deeply bound states is, to a good approximation, simply related to the Sommerfeld enhancement factor.The ultrarelativistic limit of Kerrhttps://zbmath.org/1541.830322024-09-27T17:47:02.548271Z"Adamo, Tim"https://zbmath.org/authors/?q=ai:adamo.tim"Cristofoli, Andrea"https://zbmath.org/authors/?q=ai:cristofoli.andrea"Tourkine, Piotr"https://zbmath.org/authors/?q=ai:tourkine.piotrSummary: The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by \textit{H. Balasin} and \textit{H. Nachbagauer} [Classical Quantum Gravity 13, No. 4, 731--737 (1996; Zbl 0851.53072)], does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.Reflected entropy for communicating black holes. I: Karch-Randall braneworldshttps://zbmath.org/1541.830332024-09-27T17:47:02.548271Z"Afrasiar, Mir"https://zbmath.org/authors/?q=ai:afrasiar.mir"Basak, Jaydeep Kumar"https://zbmath.org/authors/?q=ai:basak.jaydeep-kumar"Chandra, Ashish"https://zbmath.org/authors/?q=ai:chandra.ashish"Sengupta, Gautam"https://zbmath.org/authors/?q=ai:sengupta.gautamSummary: We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in \(BCFT_2\)s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the \(AdS_3/BCFT_2\) scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.Escaping the interiors of pure boundary-state black holeshttps://zbmath.org/1541.830342024-09-27T17:47:02.548271Z"Almheiri, Ahmed"https://zbmath.org/authors/?q=ai:almheiri.ahmed"Mousatov, Alexandros"https://zbmath.org/authors/?q=ai:mousatov.alexandros"Shyani, Milind"https://zbmath.org/authors/?q=ai:shyani.milindSummary: We consider a class of pure black hole microstates and demonstrate that they can be made escapable by turning on certain double trace deformations in the CFT. These microstates are dual to BCFT states prepared via a Euclidean path integral starting from a boundary in Euclidean time. These states are dual to black holes in the bulk with an End-of-the-World brane; a codimension one timelike boundary of the spacetime behind the horizon. We show that by tuning the sign of the coupling of the double trace operator to the boundary conditions on the brane the deformation injects negative energy into the black hole causing a time advance for signals behind the horizon. We demonstrate how the property of escapability in the considered microstates follows immediately from the traversability of deformed wormholes. We briefly comment on reconstruction of the black hole interior and state dependence.Chaos and pole-skipping in a simply spinning plasmahttps://zbmath.org/1541.830352024-09-27T17:47:02.548271Z"Amano, Markus A. G."https://zbmath.org/authors/?q=ai:amano.markus-a-g"Blake, Mike"https://zbmath.org/authors/?q=ai:blake.mike"Cartwright, Casey"https://zbmath.org/authors/?q=ai:cartwright.casey"Kaminski, Matthias"https://zbmath.org/authors/?q=ai:kaminski.matthias"Thompson, Anthony P."https://zbmath.org/authors/?q=ai:thompson.anthony-pSummary: We study the relationship between many-body quantum chaos and energy dynamics in holographic quantum field theory states dual to the simply-spinning Myers-Perry-\(\mathrm{AdS}_5\) black hole. The enhanced symmetry of such black holes allows us to provide a thorough examination of the phenomenon of pole-skipping, that is significantly simpler than a previous analysis of quantum field theory states dual to the Kerr-\(\mathrm{AdS}_4\) solution. In particular we give a general proof of pole-skipping in the retarded energy density Green's function of the dual quantum field theory whenever the spatial profile of energy fluctuations satisfies the shockwave equation governing the form of the OTOC. Furthermore, in the large black hole limit we are able to obtain a simple analytic expression for the OTOC for operator configurations on Hopf circles, and demonstrate that the associated Lyapunov exponent and butterfly velocity are robustly related to the locations of a family of pole-skipping points in the energy response. Finally, we note that in contrast to previous studies, our results are valid for any value of rotation and we are able to numerically demonstrate that the dispersion relations of sound modes in the energy response explicitly pass through our pole-skipping locations.Non-BPS bubbling geometries in \(\mathrm{AdS}_3\)https://zbmath.org/1541.830362024-09-27T17:47:02.548271Z"Bah, Ibrahima"https://zbmath.org/authors/?q=ai:bah.ibrahima"Heidmann, Pierre"https://zbmath.org/authors/?q=ai:heidmann.pierreSummary: We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to \(\mathrm{AdS}_3\times\mathrm{S}^3\times\mathrm{T}^4\) in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other \(\mathrm{AdS}_D\times\mathcal{C}\) settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitly derive solutions by applying the charged Weyl formalism that we have previously developed. These are sourced internally by a chain of bolts that correspond to regions where the orbits of the commuting Killing vectors collapse smoothly. We show that these geometries can be interpreted as non-BPS \(\mathrm{T}^4\) and \(\mathrm{S}^3\) deformations on global \(\mathrm{AdS}_3\times\mathrm{S}^3\times\mathrm{T}^4\) that are located at the center of \(\mathrm{AdS}_3\). These non-BPS deformations can be made arbitrarily small and should therefore correspond to non-supersymmetric operators in the D1-D5 CFT. Finally, we also construct interesting bound states of non-extremal BTZ black holes connected by regular bolts.Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fieldshttps://zbmath.org/1541.830382024-09-27T17:47:02.548271Z"Cárdenas, Marcela"https://zbmath.org/authors/?q=ai:cardenas.marcela"Fuentealba, Oscar"https://zbmath.org/authors/?q=ai:fuentealba.oscar"Martínez, Cristián"https://zbmath.org/authors/?q=ai:martinez.cristian"Troncoso, Ricardo"https://zbmath.org/authors/?q=ai:troncoso.ricardoSummary: Einstein gravity minimally coupled to a scalar field with a two-parameter Higgs-like self-interaction in three spacetime dimensions is recast in terms of a Chern-Simons form for the algebra \(g^+ \oplus g^-\) where, depending on the sign of the self-interaction couplings, \(g^\pm\) can be \(so(2, 2)\), \(so(3, 1)\) or \(iso(2, 1)\). The field equations can then be expressed through the field strength of non-flat composite gauge fields, and conserved charges are readily obtained from boundary terms in the action that agree with those of standard Chern-Simons theory for pure gravity, but with non-flat connections. Regularity of the fields then amounts to requiring the holonomy of the connections along contractible cycles to be trivial. These conditions are automatically fulfilled for the scalar soliton and allow to recover the Hawking temperature and chemical potential in the case of the rotating hairy black holes presented here, whose entropy can also be obtained by the same formula that holds in the case of a pure Chern-Simons theory. In the conformal (Jordan) frame the theory is described by General Relativity with cosmological constant conformally coupled to a self-interacting scalar field, and its formulation in terms of a Chern-Simons form for suitably composite gauge fields is also briefly addressed.Words to describe a black holehttps://zbmath.org/1541.830402024-09-27T17:47:02.548271Z"Chang, Chi-Ming"https://zbmath.org/authors/?q=ai:chang.chi-ming"Lin, Ying-Hsuan"https://zbmath.org/authors/?q=ai:lin.ying-hsuanSummary: We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.JT gravity from partial reduction and defect extremal surfacehttps://zbmath.org/1541.830432024-09-27T17:47:02.548271Z"Deng, Feiyu"https://zbmath.org/authors/?q=ai:deng.feiyu"An, Yu-Sen"https://zbmath.org/authors/?q=ai:an.yu-sen"Zhou, Yang"https://zbmath.org/authors/?q=ai:zhou.yangSummary: We propose the three-dimensional counterpart for Jackiw-Teitelboim gravity coupled with \(\mathrm{CFT}_2\) bath based on partial reduction. The three-dimensional counterpart is classical AdS gravity with a defect brane which has small fluctuation in transverse direction. We derive full Jackiw-Teitelboim gravity action by considering the transverse fluctuation as a dilaton field. We demonstrate that the fine-grained entropy computed from island formula precisely agrees with that computed from defect extremal surface. Our construction provides a Lorentzian higher dimensional counterpart for Jackiw-Teitelboim gravity glued to a bath and therefore offers a framework to study problems such as black hole information paradox.On supersymmetric multipole ratioshttps://zbmath.org/1541.830442024-09-27T17:47:02.548271Z"Ganchev, Bogdan"https://zbmath.org/authors/?q=ai:ganchev.bogdan"Mayerson, Daniel R."https://zbmath.org/authors/?q=ai:mayerson.daniel-rSummary: Four-dimensional supersymmetric black holes are static and so have all vanishing multipoles (except the mass monopole). Nevertheless, it is possible to define finite multipole ratios for these black holes, by taking the ratio of (finite) multipoles of supersymmetric multicentered geometries and then taking the black hole scaling limit of the multipole ratios within these geometries. An alternative way to calculate these multipole ratios is to deform the supersymmetric black hole slightly into a non-extremal, rotating black hole, calculate the multipole ratios of this altered black hole, and then take the supersymmetric limit of the ratios. Bena and Mayerson observed that for a class of microstate geometries, these two a priori completely different methods give spectacular agreement for the resulting supersymmetric black hole multipole ratios. They conjectured that this agreement is due to the smallness of the entropy parameter for these black holes. We correct this conjecture and give strong evidence supporting a more refined conjecture, which is that the agreement of multipole ratios as calculated with these two different methods is due to both the microstate geometry and its corresponding black hole having a property we call ``large dipole'', which can be interpreted as their center of mass being far away from its apparent center.Noncommutativity and logarithmic correction to the black hole entropyhttps://zbmath.org/1541.830452024-09-27T17:47:02.548271Z"Gupta, Kumar S."https://zbmath.org/authors/?q=ai:gupta.kumar-sankar"Jurić, Tajron"https://zbmath.org/authors/?q=ai:juric.tajron"Samsarov, Andjelo"https://zbmath.org/authors/?q=ai:samsarov.andjelo"Smolić, Ivica"https://zbmath.org/authors/?q=ai:smolic.ivicaSummary: We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a \(\kappa\)-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding at least some quantum effects in curved spacetime, although additional contributions will appear when the NC effects are fully incorporated in a gravity theory.Novel black holes in higher derivative gravityhttps://zbmath.org/1541.830472024-09-27T17:47:02.548271Z"Huang, Yang"https://zbmath.org/authors/?q=ai:huang.yang"Liu, Dao-Jun"https://zbmath.org/authors/?q=ai:liu.daojun"Zhang, Hongsheng"https://zbmath.org/authors/?q=ai:zhang.hongshengSummary: We find a class of novel black holes in higher derivative theory. The novel black holes follow behavior of Schwarzschild ones at large mass limit, while dramatically differentiate from Schwarzschild ones for little holes because of the effects which may root in quantum gravity. The temperature of the hole takes maximum for a specific mass, which is related to the new sale introduced in the higher derivative theory, and goes to zero at little mass limit. This property leads to a significant observation that the novel black hole may be a candidate for dark matters evading constraint from \(\gamma\)-ray burst.Scrambling and entangling spinning particleshttps://zbmath.org/1541.830492024-09-27T17:47:02.548271Z"Hung, Ling-Yan"https://zbmath.org/authors/?q=ai:hung.ling-yan"Ji, Kaixin"https://zbmath.org/authors/?q=ai:ji.kaixin"Wang, Tianheng"https://zbmath.org/authors/?q=ai:wang.tianhengSummary: In this paper we revisit the gravitational eikonal amplitudes of two scattering spinning particles and inspect their scrambling power in the spin spaces that is quantified through the tripartite information. We found that in the non-relativistic limit and a special high-energy limit the leading contribution is a quantity that is universal and theory independent. The minimal coupling is singled out with minimal scrambling in a different high momenta limit. We also inspected the initial state dependence of entanglement generation and found that the spin coherent state with vanishing spin may not necessarily be the hardest to entangle. Interestingly, among a family of mixed states, the only P-rep state there known to be the best approximation of classical mixed states was singled out as one with minimal entanglement generated.Non-isometric quantum error correction in gravityhttps://zbmath.org/1541.830502024-09-27T17:47:02.548271Z"Kar, Arjun"https://zbmath.org/authors/?q=ai:kar.arjunSummary: We construct and study an ensemble of non-isometric error correcting codes in a toy model of an evaporating black hole in two-dimensional dilaton gravity. In the preferred bases of Euclidean path integral states in the bulk and Hamiltonian eigenstates in the boundary, the encoding map is proportional to a linear transformation with independent complex Gaussian random entries of zero mean and unit variance. Using measure concentration, we show that the typical such code is very likely to preserve pairwise inner products in a set \(S\) of states that can be subexponentially large in the microcanonical Hilbert space dimension of the black hole. The size of this set also serves as an upper limit on the bulk effective field theory Hilbert space dimension. Similar techniques are used to demonstrate the existence of state-specific reconstructions of \(S\)-preserving code space unitary operators. State-specific reconstructions on subspaces exist when they are expected to by entanglement wedge reconstruction. We comment on relations to complexity theory and the breakdown of bulk effective field theory.Complementarity and the unitarity of the black hole \(S\)-matrixhttps://zbmath.org/1541.830512024-09-27T17:47:02.548271Z"Kim, Isaac H."https://zbmath.org/authors/?q=ai:kim.isaac-h"Preskill, John"https://zbmath.org/authors/?q=ai:preskill.johnSummary: Recently, \textit{C. Akers} et al. [``The black hole interior from non-isometric codes and complexity'', Preprint, \url{arXiv:2207.06536}] proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole \(S\)-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the \(S\)-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the \(S\)-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the \(S\)-matrix of an evaporating black hole has polynomial computational complexity.Encoding beyond cosmological horizons in de Sitter JT gravityhttps://zbmath.org/1541.830532024-09-27T17:47:02.548271Z"Levine, Adam"https://zbmath.org/authors/?q=ai:levine.adam-simon"Shaghoulian, Edgar"https://zbmath.org/authors/?q=ai:shaghoulian.edgarSummary: Black hole event horizons and cosmological event horizons share many properties, making it natural to ask whether our recent advances in understanding black holes generalize to cosmology. To this end, we discuss a paradox that occurs if observers can access what lies beyond their cosmological horizon in the same way that they can access what lies beyond a black hole horizon. In particular, distinct observers with distinct horizons may encode the same portion of spacetime, violating the no-cloning theorem of quantum mechanics. This paradox is due precisely to the observer-dependence of the cosmological horizon -- the sharpest difference from a black hole horizon -- although we will argue that the gravity path integral avoids the paradox in controlled examples.Why is black hole entropy affected by rotation?https://zbmath.org/1541.830542024-09-27T17:47:02.548271Z"McInnes, Brett"https://zbmath.org/authors/?q=ai:mcinnes.brettSummary: It is well known that an asymptotically flat four-dimensional Kerr black hole has a smaller (specific) entropy than a Schwarzschild black hole of the same mass. We show here that the same is true if the temperature, rather than the mass, is held fixed; and we also show that an asymptotically \(\mathrm{AdS}_5\)-Kerr black hole has a smaller specific entropy than an \(\mathrm{AdS}_5\)-Schwarzschild black hole of the same temperature, except in a negligibly small class of special examples. The \(\mathrm{AdS}_5\)-Kerr case is particularly interesting, because here the gauge-gravity duality applies; if we further accept that there is a useful analogy between the strongly coupled field theories dual to AdS black holes and the best-understood example of a strongly coupled fluid (the Quark-Gluon Plasma), then we can apply QGP theory to predict the behaviour of black hole entropy in this case. The prediction agrees with our study of \(\mathrm{AdS}_5\)-Kerr entropy. The hope is that such results might lead ultimately to an identification of black hole microstates.JT gravity and near-extremal thermodynamics for Kerr black holes in \(AdS_{4, 5}\) for rotating perturbationshttps://zbmath.org/1541.830552024-09-27T17:47:02.548271Z"Poojary, Rohan R."https://zbmath.org/authors/?q=ai:poojary.rohan-rSummary: We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of Kerr black holes where a linear combination of excess angular momentum \(\delta J\) and excess mass \(\delta M\) is held fixed. These correspond to processes where both the mass and the angular momenta of extremal Kerr black holes are perturbed leaving them near extremal. For the Kerr \(AdS_4\) we hold \(\delta J-\mathcal{L}\delta M = 0\) while for Myers-Perry(MP) type Kerr black hole in \(AdS_5\) we hold \(\delta J_{\varphi_{1,2}}-\mathcal{L}_{\varphi_{1, 2}}\delta M = 0\). We show that in near horizon, the 2d Jackiw-Teitelboim theory is able to capture the thermodynamics of the higher dimensional black holes at small near extremal temperatures \(T_H\). We show this by generalizing the near horizon limits found in literature by parameters \(\mathcal{L}\) and \(\mathcal{L}_{\varphi_{1, 2}}\) for the two geometries. The resulting JT theory captures the near extremal thermodynamics of such geometries provided we identify the temperature \(T_H^{(2)}\) of the near horizon \(AdS_2\) geometry to be \(T_H^{(2)} = T_H/(1-\mu\mathcal{L})\) for 4d Kerr and \(T_H^{(2)} = T_H/(1-\mu(\mathcal{L}_{\varphi_1} + \mathcal{L}_{\varphi_2}))\) for 5d Kerr \(\mu\) is their chemical potential, with \(\mu\mathcal{L} < 1\) and \(\mu(\mathcal{L}_{\varphi_1} + \mathcal{L}_{\varphi_2}) < 1\) respectively. We also argue that such a theory embeds itself non-trivially in the higher dimensional theory dual to the Kerr geometries.Superstrata on orbifolded backgroundshttps://zbmath.org/1541.830572024-09-27T17:47:02.548271Z"Shigemori, Masaki"https://zbmath.org/authors/?q=ai:shigemori.masakiSummary: Some microstates of the Strominger-Vafa black hole are represented by smooth horizonless geometries called superstrata. The standard superstrata are deformations of \(\mathrm{AdS}_3 \times S^3\), but there are also generalizations of superstrata on the orbifold \((\mathrm{AdS}_3 \times S^3)/ \mathbb{Z}_p\). In this paper, we discuss aspects of such orbifolded superstrata. We present a CFT perspective on the structure of orbifolded superstrata, showing that they can be constructed in a \(p\)-covering space of the orbifold CFT just as the standard superstrata. We also explicitly write down and study the geometry of the orbifolded superstrata, focusing on the difference from the non-orbifold case, \(p = 1\). We discuss further generalization of superstrata to the ones on a fractional spectral flow of \((\mathrm{AdS}_3\times S^3)/\mathbb{Z}_p\). This generalization involves new fractional mode excitations of the CFT side. We estimate the number of those generalized superstrata, and show that their entropy is too small to account for the Strominger-Vafa entropy. We will discuss some implications of this result, related to the typical microstates of the black hole and the relevant supersymmetry index.Would quantum coherence be increased by curvature effect in de Sitter space?https://zbmath.org/1541.830612024-09-27T17:47:02.548271Z"Wu, Shu-Min"https://zbmath.org/authors/?q=ai:wu.shu-min"Wang, Chun-Xu"https://zbmath.org/authors/?q=ai:wang.chunxu"Liu, Dan-Dan"https://zbmath.org/authors/?q=ai:liu.dandan"Huang, Xiao-Li"https://zbmath.org/authors/?q=ai:huang.xiaoli"Zeng, Hao-Sheng"https://zbmath.org/authors/?q=ai:zeng.haoshengSummary: We study the quantum coherence in de Sitter space for the bipartite system of Alice and Bob who initially share an entangled state between the two modes of a free massive scalar field. It is shown that the space-curvature effect can produce both local coherence and correlated coherence, leading to the increase of the total coherence of the bipartite system. These results are sharp different from the Unruh effect or Hawking effect, which, in the single mode approximation, cannot produce local coherence and at the same time destroy correlated coherence, leading to the decrease of the total coherence of the bipartite systems. Interestingly, we find that quantum coherence has the opposite behavior compared with the quantum correlation in de Sitter space. We also find that quantum coherence is most severely affected by the curvature effect of de Sitter space for the cases of conformal invariance and masslessness. Our result reveals the difference between the curvature effect in the de Sitter space and the Unruh effect in Rindler spacetime or the Hawking effect in black hole spacetime on quantum coherence.A geometrical approach to nontrivial topology via exotic spinorshttps://zbmath.org/1541.830622024-09-27T17:47:02.548271Z"da Silva, J. M. Hoff"https://zbmath.org/authors/?q=ai:hoff-da-silva.j-m|hoff-da-silva.julio-marny|da-silva.julio-m-hoff"Cavalcanti, R. T."https://zbmath.org/authors/?q=ai:cavalcanti.rogerio-t|cavalcanti.rafael-t"Beghetto, D."https://zbmath.org/authors/?q=ai:beghetto.d"da Rocha, G. M. Caires"https://zbmath.org/authors/?q=ai:da-rocha.g-m-cairesSummary: Exotic spinors arise in non-simply connected base manifolds due to the nonequivalent spinor structure. The dynamics of exotic spinors are endowed with an additional differential factor. In this work, we merge the exotic spinor scenario with Cartan's spinor viewpoint, according to which a given spacetime point is understood as a kind of composition of spinor entries. As a result, we arrive at a geometrical setup in which the Minkowski metric is perturbed by elements reflecting the nontrivial topology. Such corrections shall be felt by any physical system studied with the resulting bilinear form. Within the flat spacetime context, we investigate quasinormal modes arising from the interference of nontrivial topology in the scalar field dispersion relation.GJMS-like operators on symmetric 2-tensors and their gravitational dualshttps://zbmath.org/1541.830772024-09-27T17:47:02.548271Z"Aros, R."https://zbmath.org/authors/?q=ai:aros.rodrigo"Bugini, F."https://zbmath.org/authors/?q=ai:bugini.f"Diaz, D. E."https://zbmath.org/authors/?q=ai:diaz.d-eSummary: We study a family of higher-derivative conformal operators \(P_{2k}^{(2)}\) acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars.
We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators \(P_{2k}^{(2)}\) in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors \(P_{2k}^{(1)}\) is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part.
Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.A deformed IR: a new IR fixed point for four-dimensional holographic theorieshttps://zbmath.org/1541.830782024-09-27T17:47:02.548271Z"Horowitz, Gary T."https://zbmath.org/authors/?q=ai:horowitz.gary-t"Kolanowski, Maciej"https://zbmath.org/authors/?q=ai:kolanowski.maciej"Santos, Jorge E."https://zbmath.org/authors/?q=ai:santos.jorge-eSummary: In holography, the IR behavior of a quantum system at nonzero density is described by the near horizon geometry of an extremal charged black hole. It is commonly believed that for systems on \(S^3\), this near horizon geometry is \(\mathrm{AdS}_2 \times S^3\). We show that this is not the case: generic static, nonspherical perturbations of \(\mathrm{AdS}_2 \times S^3\) blow up at the horizon, showing that it is not a stable IR fixed point. We then construct a new near horizon geometry which is invariant under only SO(3) (and not SO(4)) symmetry and show that it is stable to SO(3)-preserving perturbations (but not in general). We also show that an open set of nonextremal, SO(3)-invariant charged black holes develop this new near horizon geometry in the limit \(T\rightarrow0\). Our new IR geometry still has \(\mathrm{AdS}_2\) symmetry, but it is warped over a deformed sphere. We also construct many other near horizon geometries, including some with no rotational symmetries, but expect them all to be unstable IR fixed points.Holographic study of \(T\bar{T}\) like deformed HV QFTs: holographic entanglement entropyhttps://zbmath.org/1541.830792024-09-27T17:47:02.548271Z"Jeong, Hyun-Sik"https://zbmath.org/authors/?q=ai:jeong.hyun-sik"Pan, Wen-Bin"https://zbmath.org/authors/?q=ai:pan.wen-bin"Sun, Ya-Wen"https://zbmath.org/authors/?q=ai:sun.yawen"Wang, Yuan-Tai"https://zbmath.org/authors/?q=ai:wang.yuan-taiSummary: We study the \((d + 2)\)-dimensional Hyperscaling Violating (HV) geometries in the presence of both a finite temperature \(T\) and a UV cutoff \(r_c\). This gravitational system is conjectured to be dual to \(T\bar{T}\) like deformed HV QFTs. We consider the representative quantum entanglement quantity in holography, i.e. the entanglement entropy \(S(A)\), and perform a complete analysis in all possible parameter ranges of the hyperscaling violation exponent \(\theta\) and the critical dynamical exponent \(z\) to study the effect of the temperature and the cutoff. We find that the temperature has a universal effect independent of the parameters: it enhances \(S(A)\) in the small cutoff limit, while it is irrelevant in the large cutoff limit. For the cutoff effect, we find that the cutoff monotonically suppresses \(S(A)\) where its behavior depends on the parameter range. As an application of the finite temperature analysis, we study the first law of entanglement entropy, \(S_T - S_{T = 0}\sim\ell^\lambda\), in the small subsystem size \(\ell\) limit. We find that \(\lambda\) interpolates between \(\lambda = 1 + z\) in the small cutoff and \(\lambda = 3\) in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at \(z = d - \theta\) and discuss its possibility of comparison with the field theoretic result.A solvable model of flat space holographyhttps://zbmath.org/1541.830812024-09-27T17:47:02.548271Z"Rosso, Felipe"https://zbmath.org/authors/?q=ai:rosso.felipeSummary: We propose an explicit realization of flat space holography in two dimensions where both sides of the duality are independently defined and the boundary theory is completely solvable. In the bulk, we define a novel \(\mathcal{N} = 1\) flat space supergravity theory and exactly compute the full topological expansion of its Euclidean partition function with an arbitrary number of boundaries. On the boundary, we consider a double scaled Hermitian random matrix model with Gaussian potential and use the loop equations to show it independently reproduces the bulk partition function to all orders in the topological expansion. The non-perturbative completion of the supergravity theory provided by the solvable Gaussian matrix model allows for the exact, and in many cases analytic, computation of observables in flat space quantum gravity.Dynamical stability from quasi normal modes in 2nd, 1st and 0th order holographic superfluid phase transitionshttps://zbmath.org/1541.830822024-09-27T17:47:02.548271Z"Zhao, Zi-Qiang"https://zbmath.org/authors/?q=ai:zhao.ziqiang"Zhang, Xing-Kun"https://zbmath.org/authors/?q=ai:zhang.xing-kun"Nie, Zhang-Yu"https://zbmath.org/authors/?q=ai:nie.zhang-yuSummary: We study a simple extension of the original Hartnoll, Herzog and Horowitz (HHH) holographic superfluid model with two nonlinear scalar self-interaction terms \(\lambda|\psi|^4\) and \(\tau|\psi|^6\) in the probe limit. Depending on the value of \(\lambda\) and \(\tau\), this setup allows us to realize a large spectrum of holographic phase transitions which are 2nd, 1st and 0th order as well as the ``cave of wind'' phase transition. We speculate the landscape pictures and explore the near equilibrium dynamics of the lowest quasinormal modes (QNMs) across the whole phase diagram at both zero and finite wave-vector. We find that the zero wave-vector results of QNMs correctly present the stability of the system under homogeneous perturbations and perfectly agree with the landscape analysis of homogeneous configurations in canonical ensemble. The zero wave-vector results also show that a 0th order phase transition cannot occur since it always corresponds to a global instability of the whole system. The finite wave-vector results show that under inhomogeneous perturbations, the unstable region is larger than that under only homogeneous perturbations, and the new boundary of instability match with the turning point of condensate curve in grand canonical ensemble, indicating a new explanation from the subsystem point of view. The additional unstable section also perfectly match the section with negative value of charge susceptibility.Quantum current dissipation in superconducting strings and vortonshttps://zbmath.org/1541.830832024-09-27T17:47:02.548271Z"Abe, Yoshihiko"https://zbmath.org/authors/?q=ai:abe.yoshihiko"Hamada, Yu"https://zbmath.org/authors/?q=ai:hamada.yu"Saji, Kota"https://zbmath.org/authors/?q=ai:saji.kota"Yoshioka, Koichi"https://zbmath.org/authors/?q=ai:yoshioka.koichiSummary: In this work, the current stability is discussed for cosmic strings with the bosonic superconductivity. A non-vanishing curvature of string generally induce the quantum instability of the current-carrying particle. Its decay rates are explored for various types of model parameters, curved string shapes, and decay processes. As a cosmological application, the stability is examined for superconducting strings in the string network and also for cosmic vortons by evaluating their cosmological evolution. The zero mode and hence the vorton cannot be stable in various cases, e.g., with a hierarchy between the current-carrying particle mass off the string and the string tension or with sizable couplings of the current-carrying particle to light species such as the Standard Model particles.Self-binding energies in AdShttps://zbmath.org/1541.830852024-09-27T17:47:02.548271Z"Andriolo, Stefano"https://zbmath.org/authors/?q=ai:andriolo.stefano"Michel, Marco"https://zbmath.org/authors/?q=ai:michel.marco"Palti, Eran"https://zbmath.org/authors/?q=ai:palti.eranSummary: The Positive Binding Conjecture is a proposed formulation of the Weak Gravity Conjecture appropriate to Anti de-Sitter (AdS) space. It proposes that in a consistent gravitational theory, with a U(1) gauge symmetry, there must exist a charged particle with non-negative self-binding energy. In order to formulate this as a constraint on a given effective theory, we calculate the self-binding energy for a charged particle in \(\mathrm{AdS}_4\) and \(\mathrm{AdS}_5\). In particular, we allow it to couple to an additional scalar field of arbitrary mass. Unlike the flat-space case, even when the scalar field is massive it contributes significantly to the binding energy, and therefore is an essential component of the conjecture. In \(\mathrm{AdS}_5\), we give analytic expressions for the self-binding energy for the cases when the scalar field is massless and when it saturates the Breitenlohner-Freedman (BF) bound, and in \(\mathrm{AdS}_4\) when it is massless. We show that the massless case reproduces the flat-space expressions in the large AdS radius limit, and that both analytic cases lead to vanishing total self-binding energy for BPS particles in example supersymmetric models. For other masses of the scalar we give numerical expressions for its contribution to the self-binding energy.D4-branes wrapped on four-dimensional orbifolds through consistent truncationhttps://zbmath.org/1541.830862024-09-27T17:47:02.548271Z"Couzens, Christopher"https://zbmath.org/authors/?q=ai:couzens.christopher"Kim, Hyojoong"https://zbmath.org/authors/?q=ai:kim.hyojoong"Kim, Nakwoo"https://zbmath.org/authors/?q=ai:kim.nakwoo"Lee, Yein"https://zbmath.org/authors/?q=ai:lee.yein"Suh, Minwoo"https://zbmath.org/authors/?q=ai:suh.minwooSummary: We construct a consistent truncation of six-dimensional matter coupled \(F(4)\) gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known \(\mathrm{AdS}_2\times\boldsymbol{\Sigma}_1\) solutions giving rise to four-dimensional orbifold solutions, \(\mathrm{AdS}_2\times\boldsymbol{\Sigma}_1\ltimes\boldsymbol{\Sigma}_2\). We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional \(\mathrm{U}(1)^2\)-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically \(\mathrm{AdS}_6\) black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional \(\mathrm{USp}(2N)\) theory living on a stack of D4--D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein-Hawking entropy holographically.Islands and light gravitons in type IIB string theoryhttps://zbmath.org/1541.830872024-09-27T17:47:02.548271Z"Demulder, Saskia"https://zbmath.org/authors/?q=ai:demulder.saskia"Gnecchi, Alessandra"https://zbmath.org/authors/?q=ai:gnecchi.alessandra"Lavdas, Ioannis"https://zbmath.org/authors/?q=ai:lavdas.ioannis"Lüst, Dieter"https://zbmath.org/authors/?q=ai:lust.dieterSummary: We consider the setup of a black hole in \(\mathrm{AdS}_4\) coupled to an external bath, embedded in type IIB string theory. We study quantum extremal islands in these backgrounds, in relation to the existence of a massive graviton. Using explicit results of the microscopic embedding of \(\mathrm{AdS}_4\) massive gravity in string theory, we investigate whether it is possible to achieve backgrounds with extremal islands, in which the lowest lying graviton is only slightly massive. For certain regions of the microscopic parameters, the graviton mass can be computed explicitly, and we explain how it directly affects the existence and the properties of the islands. We also show that islands can in principle exist within the regime of validity of the massive gravity effective field theory. However we see via numerical computations that the existence of quantum extremal islands at zero temperature is highly constrained, also when the dilaton is allowed to vary, so that the mass of the graviton cannot be made arbitrarily light. At finite temperature, we also identify a critical parameter, above and below which islands still exist but exhibit a different behavior. Our work supports recent proposals that the unitary evolution of black holes in higher dimensions, and more precisely their Page curve, relies on the presence of a massive graviton in the effective theory.A worldsheet description of instant folded stringshttps://zbmath.org/1541.830892024-09-27T17:47:02.548271Z"Hashimoto, Akikazu"https://zbmath.org/authors/?q=ai:hashimoto.akikazu"Itzhaki, Nissan"https://zbmath.org/authors/?q=ai:itzhaki.nissan"Peleg, Uri"https://zbmath.org/authors/?q=ai:peleg.uriSummary: Time-like linear dilaton backgrounds admit a classical solution that describes a closed folded string that is created at an instant. We refer to such strings as Instant Folded Strings (IFS). We study an exact worldsheet CFT description of an IFS that involves two vertex operators which describe two open string modes that propagate on a time-like FZZT-brane, which plays the role of a regulator to the IFS. We take advantage of this description to calculate the most basic quantity associated with IFSs -- their production rate. Some implications of this calculation to stringy cosmology and black hole interior are briefly discussed.Heterotic de Sitter beyond modular symmetryhttps://zbmath.org/1541.830902024-09-27T17:47:02.548271Z"Leedom, Jacob M."https://zbmath.org/authors/?q=ai:leedom.jacob-m"Righi, Nicole"https://zbmath.org/authors/?q=ai:righi.nicole"Westphal, Alexander"https://zbmath.org/authors/?q=ai:westphal.alexanderSummary: We study the vacua of \(4d\) heterotic toroidal orbifolds using effective theories consisting of an overall Kähler modulus, the dilaton, and non-perturbative corrections to both the superpotential and Kähler potential that respect modular invariance. We prove three de Sitter no-go theorems for several classes of vacua and thereby substantiate and extend previous conjectures. Additionally, we provide evidence that extrema of the scalar potential can occur inside the \(\mathrm{PSL}(2, \mathbb{Z})\) fundamental domain of the Kähler modulus, in contradiction of a separate conjecture. We also illustrate a loophole in the no-go theorems and determine criteria that allow for metastable de Sitter vacua. Finally, we identify inherently stringy non-perturbative effects in the dilaton sector that could exploit this loophole and potentially realize de Sitter vacua.Supersymmetric solitons in gauged \(\mathcal{N} = 8\) supergravityhttps://zbmath.org/1541.830932024-09-27T17:47:02.548271Z"Anabalón, Andrés"https://zbmath.org/authors/?q=ai:anabalon.andres"Gallerati, Antonio"https://zbmath.org/authors/?q=ai:gallerati.antonio"Ross, Simon"https://zbmath.org/authors/?q=ai:ross.simon-f"Trigiante, Mario"https://zbmath.org/authors/?q=ai:trigiante.marioSummary: We consider soliton solutions in \(\mathrm{AdS}_4\) with a flat slicing and Wilson loops around one cycle. We study the phase structure and find the ground state and identify supersymmetric solutions as a function of the Wilson loops. We work in the context of a scalar field truncation of gauged \(\mathcal{N} = 8\) supergravity, where all the dilatons are equal and all the axions vanish in the STU model. In this theory, we construct new soliton solutions parameterized by two Wilson lines. We find that there is a degeneracy of supersymmetric solutions. We also show that, for alternate boundary conditions, there exists a non-supersymmetric soliton solution with energy lower than the supersymmetric one.B-RNS-GSS heterotic string in curved backgroundshttps://zbmath.org/1541.830942024-09-27T17:47:02.548271Z"Berkovits, Nathan"https://zbmath.org/authors/?q=ai:berkovits.nathan-j"Chandia, Osvaldo"https://zbmath.org/authors/?q=ai:chandia.osvaldo"Gomide, João"https://zbmath.org/authors/?q=ai:gomide.joao"Martins, Lucas N. S."https://zbmath.org/authors/?q=ai:martins.lucas-n-sSummary: The recently established B-RNS-GSS formalism is extended for the description of the heterotic superstring in curved backgrounds. We propose a generalized action and BRST charge defined in the small Hilbert space with the standard form of an \(\mathcal{N} = (1, 0)\) worldsheet superconformal theory with superconformal generator \(G\) and stress tensor \(T\). We show that \(\{G, G\} = -2T\) implies the D=10 N=1 supergravity and super-Yang-Mills equations of motion, as well as holomorphicity of the BRST charge.Holography for \(\mathcal{N} = 4\) on \(\mathbb{RP}^4\)https://zbmath.org/1541.830952024-09-27T17:47:02.548271Z"Caetano, João"https://zbmath.org/authors/?q=ai:caetano.joao"Rastelli, Leonardo"https://zbmath.org/authors/?q=ai:rastelli.leonardoSummary: We propose a holographic description of \(\mathcal{N} = 4\) super Yang-Mills on the four-dimensional real projective space \(\mathbb{RP}^4\). We first construct the dual background in the framework of five-dimensional \(\mathcal{N} = 8\) gauged supergravity, and then uplift it to a new one-half BPS solution of type IIB supergravity. A salient feature of our solution is the presence of a bulk naked singularity whose local behavior resembles that of an \(O1_-\) plane in flat space.Double-copy towards supergravity inflation with \(\alpha\)-attractor modelshttps://zbmath.org/1541.830962024-09-27T17:47:02.548271Z"Carrasco, John Joseph M."https://zbmath.org/authors/?q=ai:carrasco.john-joseph-m"Lewandowski, Matthew"https://zbmath.org/authors/?q=ai:lewandowski.matthew"Pavao, Nicolas H."https://zbmath.org/authors/?q=ai:pavao.nicolas-hSummary: Key to the simplicity of supergravity \(\alpha\)-attractor models of inflation are Volkov-Akulov fermions, often in the form of nilpotent superfields. Here we explore the possibility of using the double-copy to construct theories of Dirac-Born-Infeld-Volkov-Akulov (DBIVA) coupled to supergravity. A color-dual bootstrap admits scattering amplitudes involving pions and vectors through five-point tree-level order by order in mass-dimension, but requires the introduction of a \(\operatorname{Tr}(F^3)\) operator. Gauge theories with this operator were recently found to require a tower of higher-derivative operators to be compatible with the duality between color and kinematics. Adjoint-type double-copy construction at its most conservative seems to require the UV completion of DBIVA + pure Poincaré supergravity scattering amplitudes to a family of theories involving DBIVA-like particles coupled to Weyl-Einstein supergravity. We also point out an alternative solution to color-dual gauged pions that allows adjoint double-copy without a tower of higher derivative corrections but at the cost of exchange symmetry between scalars.Perfecting one-loop BCJ numerators in SYM and supergravityhttps://zbmath.org/1541.830972024-09-27T17:47:02.548271Z"Edison, Alex"https://zbmath.org/authors/?q=ai:edison.alex"He, Song"https://zbmath.org/authors/?q=ai:he.song"Johansson, Henrik"https://zbmath.org/authors/?q=ai:johansson.henrik"Schlotterer, Oliver"https://zbmath.org/authors/?q=ai:schlotterer.oliver"Teng, Fei"https://zbmath.org/authors/?q=ai:teng.fei"Zhang, Yong"https://zbmath.org/authors/?q=ai:zhang.yong.59Summary: We take a major step towards computing \(D\)-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For \(n\)-point amplitudes with either supersymmetry multiplets or generic non-supersymmetric matter in the loop, simple all-multiplicity expressions are obtained for the maximal cuts of kinematic numerators of \(n\)-gon diagrams. At \(n = 6, 7\) points with maximal supersymmetry, we extend the cubic-diagram numerators to encode all contact terms, and thus solve the long-standing problem of \textit{simultaneously} realizing the following properties: color-kinematics duality, manifest locality, optimal power counting of loop momenta, quadratic rather than linearized Feynman propagators, compatibility with double copy as well as all graph symmetries. Color-kinematics dual representations with similar properties are presented in the half-maximally supersymmetric case at \(n = 4, 5\) points. The resulting gauge-theory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.Maximally symmetric nuts in 4d \(\mathcal{N} = 2\) higher derivative supergravityhttps://zbmath.org/1541.830992024-09-27T17:47:02.548271Z"Hristov, Kiril"https://zbmath.org/authors/?q=ai:hristov.kirilSummary: We initiate a systematic study of supersymmetric backgrounds in 4d \(\mathcal{N} = 2\) Euclidean supergravity in the presence of infinite towers of higher derivative corrections. Adopting a Gibbons-Hawking view towards the evaluation of the action in terms of nuts and bolts, we consider the two maximally symmetric vacua \(\mathbb{R}^4\) and \(\mathbb{H}^4\) (Euclidean \(\mathrm{AdS}_4\)) and their unique supersymmetric deformations with (anti-) self-dual Maxwell tensors corresponding to a single nut at the center. These are the Omega background of Nekrasov-Okounkov, \(\Omega\mathbb{R}^4\), and its generalization with a cosmological constant of Martelli-Passias-Sparks, denoted \(\Omega\mathbb{H}^4\) (also known as the gravity dual of the \(\mathrm{U}(1)\times\mathrm{U}(1)\) squashed sphere). We write down the BPS configurations in the superconformal formalism in the presence of vector multiplets and derive the corresponding off- and on-shell actions. Our results provide a rigorous proof for important parts of the conjecture in [the author, J. High Energy Phys. 2022, No. 2, Paper No. 79, 56 p. (2022; Zbl 1522.83191)] and its holographic corollary in [the author, J. High Energy Phys. 2022, No. 10, Paper No. 190, 14 p. (2022; Zbl 1534.83126)], which we discuss in detail along with extensions such as the addition of hypermultiplets and the presence of conical defects.Conformal \((p, q)\) supergeometries in two dimensionshttps://zbmath.org/1541.831002024-09-27T17:47:02.548271Z"Kuzenko, Sergei M."https://zbmath.org/authors/?q=ai:kuzenko.sergei-m"Raptakis, Emmanouil S. N."https://zbmath.org/authors/?q=ai:raptakis.emmanouil-s-nSummary: We propose a superspace formulation for conformal \((p, q)\) supergravity in two dimensions as a gauge theory of the superconformal group \(\mathsf{OSp}_0(p|2; \mathbb{R})\times\mathsf{OSp}_0(q|2; \mathbb{R})\) with a flat connection. Upon degauging of certain local symmetries, this conformal superspace is shown to reduce to a conformally flat \(\mathsf{SO}(p) \times\mathsf{SO}(q)\) superspace with the following properties: (i) its structure group is a direct product of the Lorentz group and \(\mathsf{SO}(p) \times\mathsf{SO}(q)\); and (ii) the residual local scale symmetry is realised by super-Weyl transformations with an unconstrained real parameter. As an application of the formalism, we describe \(\mathcal{N}\)-extended AdS superspace as a maximally symmetric supergeometry in the \(p = q \equiv \mathcal{N}\) case. If at least one of the parameters \(p\) or \(q\) is even, alternative superconformal groups and, thus, conformal superspaces exist. In particular, if \(p = 2n\), a possible choice of the superconformal group is \(\mathsf{SU}(1, 1|n)\times\mathsf{OSp}_0(q|2; \mathbb{R})\), for \(n \neq 2\), and \(\mathsf{PSU}(1, 1|2) \times\mathsf{OSp}_0(q|2; \mathbb{R})\), when \(n = 2\). In general, a conformal superspace formulation is associated with a supergroup \(G = G_L \times G_R \), where the simple supergroups \(G_L\) and \(G_R\) can be any of the extended superconformal groups, which were classified by Günaydin, Sierra and Townsend. Degauging the corresponding conformal superspace leads to a conformally flat \(H_L \times H_R\) superspace, where \(H_L\) (\(H_R\)) is the \(R\)-symmetry subgroup of \(G_L\) (\(G_R\)). Additionally, for the \(p, q \leq 2\) cases we propose composite primary multiplets which generate the Gauss-Bonnet invariant and supersymmetric extensions of the Fradkin-Tseytlin term.Line defects as brane boxes in Gaiotto-Maldacena geometrieshttps://zbmath.org/1541.831012024-09-27T17:47:02.548271Z"Lozano, Yolanda"https://zbmath.org/authors/?q=ai:lozano.yolanda"Petri, Nicolò"https://zbmath.org/authors/?q=ai:petri.nicolo"Risco, Cristian"https://zbmath.org/authors/?q=ai:risco.cristianSummary: We construct a new family of \(\mathrm{AdS}_2 \times S^2 \times S^2\) solutions to Type IIA supergravity with 4 supercharges acting with non-Abelian T-duality on the recent class constructed in [\textit{Y. Lozano} et al., J. High Energy Phys. 2021, No. 10, Paper No. 217, 34 p. (2021; Zbl 1476.83172)]. We focus on a particular solution in this class asymptoting locally to an \(\mathrm{AdS}_5\) Gaiotto-Maldacena geometry. This solution allows for a line defect interpretation within the 4d \(\mathcal{N} = 2\) SCFT dual to this geometry, that we study in detail. We show that the defect branes, consisting on a non-trivial intersection of D2-D4-NS5-F1 branes, can be interpreted as baryon vertices within the 4d \(\mathcal{N} = 2\) SCFT, whose backreaction gives rise to the \(\mathrm{AdS}_2\) solution. We construct the explicit quiver quantum mechanics that flows in the IR to the dual SCQM, and show that it can be embedded within the quiver CFT associated to the \(\mathrm{AdS}_5\) solution. The quiver quantum mechanics arises from a brane box set-up of D2-branes stretched between perpendicular NS5-branes, that we construct from the \(\mathrm{AdS}_2\) solution. We provide non-trivial checks of our proposed duality. Our construction provides one further example of the successful applications of non-Abelian T-duality to holography, in this case in providing a very non-trivial connection between \(\mathrm{AdS}_2\) solutions, line defects and brane boxes.Unified no-scale attractorshttps://zbmath.org/1541.831442024-09-27T17:47:02.548271Z"Ellis, John"https://zbmath.org/authors/?q=ai:ellis.john-richard"Nanopoulos, Dimitri V."https://zbmath.org/authors/?q=ai:nanopoulos.dimitri-v"Olive, Keith A."https://zbmath.org/authors/?q=ai:olive.keith-a"Verner, Sarunas"https://zbmath.org/authors/?q=ai:verner.sarunasSummary: We have presented previously a general treatment of Starobinsky-like inflation in no-scale supergravity where the tensor-to-scalar ratio \(r = 3(1 - n_s)^2\), and \(n_s\) is the tilt of the scalar perturbations. In particular, we have shown how this scenario can be unified with modulus fixing, supersymmetry breaking and a small cosmological constant. In this paper we extend these constructions to inflationary models based on generalized no-scale structures. In particular, we consider alternative values of the curvature parameter, \(\alpha < 1\), as may occur if not all the complex Kähler moduli contribute to driving inflation, as well as \(\alpha > 1\), as may occur if complex structure moduli also contribute to driving inflation. In all cases, we combine these \(\alpha\)-Starobinsky inflation models with supersymmetry breaking and a present-day cosmological constant, allowing for additional contributions to the vacuum energy from stages of gauge symmetry breaking.Classical-quantum correspondence for fieldshttps://zbmath.org/1541.831972024-09-27T17:47:02.548271Z"Vachaspati, Tanmay"https://zbmath.org/authors/?q=ai:vachaspati.tanmay"Zahariade, George"https://zbmath.org/authors/?q=ai:zahariade.georgeSummary: We map the quantum problem of a free bosonic field in a space-time dependent background into a classical problem. \(N\) degrees of freedom of a real field in the quantum theory are mapped into \(2N^2\) classical simple harmonic oscillators with specific initial conditions. We discuss how this classical-quantum correspondence (CQC) may be used to evaluate quantum radiation and fully treat the backreaction of quantum fields on classical backgrounds. The technique has widespread application, including the quantum evaporation of classical breathers (``oscillons'').Fast neutrino flavor conversion: collective motion vs. decoherencehttps://zbmath.org/1541.850062024-09-27T17:47:02.548271Z"Capozzi, Francesco"https://zbmath.org/authors/?q=ai:capozzi.francesco"Raffelt, Georg"https://zbmath.org/authors/?q=ai:raffelt.georg-g"Stirner, Tobias"https://zbmath.org/authors/?q=ai:stirner.tobiasSummary: In an interacting neutrino gas, flavor coherence becomes dynamical and can propagate as a collective mode. In particular, tachyonic instabilities can appear, leading to ``fast flavor conversion'' that is independent of neutrino masses and mixing angles. On the other hand, without neutrino-neutrino interaction, a prepared wave packet of flavor coherence simply dissipates by kinematical decoherence of infinitely many non-collective modes. We reexamine the dispersion relation for fast flavor modes and show that for any wavenumber, there exists a continuum of non-collective modes besides a few discrete collective ones. So for any initial wave packet, both decoherence and collective motion occurs, although the latter typically dominates for a sufficiently dense gas. We derive explicit eigenfunctions for both collective and non-collective modes. If the angular mode distribution of electron-lepton number crosses between positive and negative values, two non-collective modes can merge to become a tachyonic collective mode. We explicitly calculate the interaction strength for this critical point. As a corollary we find that a single crossing always leads to a tachyonic instability. For an even number of crossings, no instability needs to occur.Liouville term for neutrinos: flavor structure and wave interpretationhttps://zbmath.org/1541.850082024-09-27T17:47:02.548271Z"Stirner, Tobias"https://zbmath.org/authors/?q=ai:stirner.tobias"Sigl, Günter"https://zbmath.org/authors/?q=ai:sigl.gunter"Raffelt, Georg"https://zbmath.org/authors/?q=ai:raffelt.georg-gSummary: Neutrino production, absorption, transport, and flavor evolution in astrophysical environments is described by a kinetic equation \(D \varrho=- i[\mathsf{H}, \varrho]+\mathcal{C}[\varrho]\). Its basic elements are generalized occupation numbers \(\varrho\), matrices in flavor space, that depend on time \(t\), space \(\mathbf{x}\), and momentum \(\mathbf{p}\). The commutator expression encodes flavor conversion in terms of a matrix \(\mathsf{H}\) of oscillation frequencies, whereas \(\mathcal{C}[\varrho]\) represents source and sink terms as well as collisions. The Liouville operator on the left hand side involves linear derivatives in \(t\), \(\mathbf{x}\) and \(\mathbf{p}\). The simplified expression \(D = \partial_t+\hat{\mathbf{p}}\cdot\partial_{\mathbf{x}}\) for ultra-relativistic neutrinos was recently questioned in that flavor-dependent velocities should appear instead of the unit vector \(\hat{\mathbf{p}}\). Moreover, a new damping term was postulated as a result. We here derive the full flavor-dependent velocity structure of the Liouville term although it appears to cause only higher-order corrections. Moreover, we argue that on the scale of the neutrino oscillation length, the kinetic equation can be seen as a first-order wave equation.On the IR-resummation in the EFTofLSShttps://zbmath.org/1541.850172024-09-27T17:47:02.548271Z"Senatore, Leonardo"https://zbmath.org/authors/?q=ai:senatore.leonardo"Trevisan, Gabriele"https://zbmath.org/authors/?q=ai:trevisan.gabrieleSummary: We propose a simplification for the IR-resummation scheme of the first author and \textit{M. Zal\-darriaga} [ibid. 2015, No. 02, Paper No. 013, 38 p. (2015; \url{doi:10.1088/1475-7516/2015/02/013})] and also include its next-to-leading order corrections coming from the tree-level three-point function of the long displacement field. First we show that the new simplified formula shares the same properties of the resummation of \textit{D. Baumann} et al. [ibid. 2012, No. 07, Paper No. 051, 81 p. (2012; \url{doi:10.1088/1475-7516/2012/07/051})]. In Fourier space, the IR-resummed power spectrum has no residual wiggles and the two-loop calculation matches the non-linear power spectrum of the Dark Sky simulation at \(z=0\) up to \(k \simeq 0.34\,h\,\mathrm{Mpc}^{-1}\) within cosmic variance. Then, we find that the additional subleading terms (although parametrically infrared-enhanced) modify the leading-order IR-resummed correlation function only in a marginal way, implying that the IR-resummation scheme can robustly predict the shape of the BAO peak.A quantum group decision model for meteorological disaster emergency response based on D-S evidence theory and Choquet integralhttps://zbmath.org/1541.910752024-09-27T17:47:02.548271Z"Yan, Shuli"https://zbmath.org/authors/?q=ai:yan.shuli"Xu, Yizhao"https://zbmath.org/authors/?q=ai:xu.yizhao"Gong, Zaiwu"https://zbmath.org/authors/?q=ai:gong.zaiwu"Herrera-Viedma, Enrique"https://zbmath.org/authors/?q=ai:herrera-viedma.enriqueSummary: In addressing complex and dynamic meteorological disaster decision-making environment, the traditional multi-attribute group decision-making domain model is often unable to effectively deal with the correlation between attributes and the mutual influence of group opinions. To overcome this challenge, this paper proposes a novel quantum framework for group decision-making, which is used to deal with the emergency situation of meteorological disaster. The model initially characterizes attribute correlations using 2-additive Choquet integrals and employs Dempster-Shafer evidence theory to both integrate information and ascertain attribute weights, and decision makers' weights are calculated based on grey relative correlation. On this basis, a quantum-like Bayesian network is developed to capture the interference among decision-makers' opinions. The alternatives are ranked by quantum probabilities computed based on Bayesian principle. Finally, a case study on meteorological disaster emergency scenario assessment is conducted to validate the proposed model's effectiveness and superiority. Additionally, its stability and practicality are confirmed through sensitivity analysis and comparative analysis.Information theory with kernel methodshttps://zbmath.org/1541.940282024-09-27T17:47:02.548271Z"Bach, Francis"https://zbmath.org/authors/?q=ai:bach.francis-rEditorial remark: No review copy delivered.Quantum-safe identity-based broadcast encryption with provable security from multivariate cryptographyhttps://zbmath.org/1541.940612024-09-27T17:47:02.548271Z"Sarkar, Ramprasad"https://zbmath.org/authors/?q=ai:sarkar.ramprasad"Mandal, Mriganka"https://zbmath.org/authors/?q=ai:mandal.mriganka"Mukhopadhyay, Sourav"https://zbmath.org/authors/?q=ai:mukhopadhyay.souravSummary: Identity-Based Broadcast Encryption (\textsf{IBBE}) is a novel concept that can efficiently and securely transmit confidential content to a group of authorized users without the traditional Public-Key Infrastructure PKI). After carefully exploring these areas, we have observed that none of the existing works have adopted the quantum-attack resistant cryptographic machinery Multivariate Public-Key Cryptography (\textsf{MPKC}) with provable security. We are the first to design a quantum-safe \textsf{IBBE} that solely relies on the \textsf{MPKC} framework. Our proposed protocol has achieved \(\mathcal{O}(n)\)-size communication bandwidth and \(n^3 \cdot\mathcal{O}\big(\max\big\{N, \delta^4\big\}\big)\)-size overhead storage without any security breach. Here, \(n\) is the number of variables for each multivariate polynomial, \(N\) represents the total number of system users, and \(\delta\) denotes a positive fixed-length. More positively, our design has achieved the adaptive INDistinguishable Chosen-Ciphertext Attack (\textsf{IND-CCA}) security in the Random Oracle Model (\textsf{ROM}) under the hardness of standard Multivariate Quadratic (\textsf{MQ}) problem. We emphasize that our system can also be immune against collusion attacks where several users come together to create an illicit decryption box.Efficient and reliable post-quantum authenticationhttps://zbmath.org/1541.940672024-09-27T17:47:02.548271Z"D'Arco, Paolo"https://zbmath.org/authors/?q=ai:darco.paolo"De Prisco, Roberto"https://zbmath.org/authors/?q=ai:de-prisco.roberto"Perez del Pozo, Angel"https://zbmath.org/authors/?q=ai:perez-del-pozo.angel-lSummary: In this paper we propose a new lightweight authentication protocol which is efficient, reliable and, properly instantiated, suitable for the post-quantum world. It is a two-level protocol, which supports unbounded message transmission. It can be useful in several settings, from the standard sender-receiver setting, to unreliable multicast and broadcast communication in networks with resource-constrained devices. The key ideas underlying our design are mainly three: the hash-chaining method, some techniques used in MAC-based authentication protocols for multicast communication, and the use of the Guy Fawkes signatures. To our knowledge, our protocol is the first one that solves the unbounded number of message transmission issue in unreliable settings. It does not lose efficiency and introduces only a constant-size overhead in message transmission, compared to solutions assuming a bounded number of message transmissions. We rigorously model the adversarial setting and show that our protocol satisfies the definition, leveraging on standard assumptions. Apart from the technical contribution, along the line, we also point out the relevance of ideas and techniques developed in the past in the area of efficient authentication, in order to provide new authentication schemes, ready for the post-quantum world.Introducing nega-Forrelation: quantum algorithms in analyzing nega-Hadamard and nega-crosscorrelation spectrahttps://zbmath.org/1541.940942024-09-27T17:47:02.548271Z"Dutta, Suman"https://zbmath.org/authors/?q=ai:dutta.suman"Maitra, Subhamoy"https://zbmath.org/authors/?q=ai:maitra.subhamoySummary: Aaronson defined Forrelation (2010) as a measure of correlation between a Boolean function \(f\) and the Walsh-Hadamard transform of another function \(g \). In a recent work, we have studied different cryptographically important spectra of Boolean functions through the lens of Forrelation. In this paper, we explore a similar kind of correlation in terms of nega-Hadamard transform. We call it nega-Forrelation and obtain a more efficient sampling strategy for nega-Hadamard transform compared to the existing results. Moreover, we present an efficient sampling strategy for nega-crosscorrelation (and consequently nega-autocorrelation) spectra too, by tweaking the nega-Forrelation technique. Finally, we connect the hidden shift finding algorithm for bent functions (Rötteler, 2010) with the Forrelation algorithm and extend it for the negabent functions.Following Forrelation -- quantum algorithms in exploring Boolean functions' spectrahttps://zbmath.org/1541.940952024-09-27T17:47:02.548271Z"Dutta, Suman"https://zbmath.org/authors/?q=ai:dutta.suman"Maitra, Subhamoy"https://zbmath.org/authors/?q=ai:maitra.subhamoy"Mukherjee, Chandra Sekhar"https://zbmath.org/authors/?q=ai:mukherjee.chandra-sekharSummary: Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al., 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation spectrum, and the autocorrelation spectrum. We introduce the existing 2-fold Forrelation formulation with bent duality-based promise problems as desirable instantiations. Next, we concentrate on the 3-fold version through two approaches. First, we judiciously set up some of the functions in 3-fold Forrelation so that given oracle access, one can sample from the Walsh Spectrum of \(f \). Using this, we obtain improved results than what one can achieve by exploiting the Deutsch-Jozsa algorithm. In turn, it has implications in resiliency checking. Furthermore, we use a similar idea to obtain a technique in estimating the cross-correlation (and thus autocorrelation) value at any point, improving upon the existing algorithms. Finally, we tweak the quantum algorithm with the superposition of linear functions to obtain a cross-correlation sampling technique. This is the first cross-correlation sampling algorithm with constant query complexity to the best of our knowledge. This also provides a strategy to check if two functions are uncorrelated of degree \(m \). We further modify this using Dicke states so that the time complexity reduces, particularly for constant values of \(m \).