Recent zbMATH articles in MSC 81Thttps://zbmath.org/atom/cc/81T2024-02-28T19:32:02.718555ZWerkzeugCancellation of spurious poles in \(N=4\) SYM: physical and geometrichttps://zbmath.org/1527.140962024-02-28T19:32:02.718555Z"Agarwala, Susama"https://zbmath.org/authors/?q=ai:agarwala.susama"Marcott, Cameron"https://zbmath.org/authors/?q=ai:marcott.cameronSummary: This paper shows that not only do the codimension one spurious poles of \(N^k M H V\) tree level diagrams in \(N=4\) SYM theory cancel in the tree level amplitude as expected, but their vanishing loci have a geometric interpretation that is tightly connected to their representation in the positive Grassmannians. In general, given a positroid variety, \(\Sigma\), and a minimal matrix representation of it in terms of independent variable valued matrices, \(M_{\mathcal{V}}\), one can define a polynomial, \(R(\mathcal{V})\) that is uniquely defined by the Grassmann necklace, \( \mathcal{I} \), of the positroid cell. The vanishing locus of \(R(\mathcal{V})\) lies on the boundary of the positive variety \(\overline{\Sigma}\setminus\Sigma\), but not all boundaries intersect the vanishing loci of a factor of \(R(\mathcal{V})\). We use this to show that the codimension one spurious poles of \(N=4\) SYM, represented in twistor space, cancel in the tree level amplitude.The amplituhedron crossing and winding numbershttps://zbmath.org/1527.140972024-02-28T19:32:02.718555Z"Blot, Xavier"https://zbmath.org/authors/?q=ai:blot.xavier"Li, Jian-Rong"https://zbmath.org/authors/?q=ai:li.jian-rong|li.jianrong\textit{N. Arkani-Hamed} and \textit{J. Trnka} [J. High Energy Phys. 2014, No. 10, Paper No. 030, 33 p. (2014; Zbl 1468.81075)] introduced the amplituhedron as the image of the totally nonnegative Grassmannian inside an ambient Grassmannian by a linear map to provide a geometric perspective in studying scattering amplitudes in physics. To understand the amplituhedron in a topological setting, \textit{N. Arkani-Hamed} et al. [J. High Energy Phys. 2018, No. 1, Paper No. 16, 41 p. (2018; Zbl 1384.81130)] associated three topological numbers to each of the ambient Grassmannian: the crossing number, the winding number, and the number of sign flips. Then, they put out a conjecture that a point of the ambient Grassmannian is in the amplituhedron if and only if it satisfies certain boundary inequalities and one of the three numbers has a definite value. Responding to the conjecture, the sign flip triangulation has been studied and significant progresses have been made while no systematic study of the crossing and winding number can be found.
The authors in this paper present some results on the association with the crossing and winding number. Specifically, they introduce a new set of equations on twistor coordinates to show that a point inside the amplituhedron has a definite winding or crossing number. This result completes one direction of the conjecture as it is well-known that a point in the amplituhedron satisfies the boundary conditions.
Reviewer: Miyeon Kwon (Platteville)On the representations of Clifford and \(\mathrm{SO}(1, 9)\) algebras for 8-component Dirac equationhttps://zbmath.org/1527.150232024-02-28T19:32:02.718555Z"Simulik, V. M."https://zbmath.org/authors/?q=ai:simulik.v-m"Vyikon, I. I."https://zbmath.org/authors/?q=ai:vyikon.i-iThe authors consider extended Clifford-Dirac gamma matrices and \(\mathrm{SO}(1,9)\) algebras by means of an eight-dimensional linear representation, from which a gamma matrix representation of dimension \(256\) is deduced, thus showing their equivalence with the Clifford algebras \(Cl(0,8)\) and \(Cl(1,7)\) over the real field. Related representations of \(\mathrm{SO}(10)\) and \(\mathrm{SO}(1,9)\) algebras are also considered as well and a detailed comparison of the obtained algebras in the space of standard 4-component Dirac spinors is provided. This construction allows the authors to generalize field equations of higher spin, with special emphasis on the case with spin \(3/2\). In this way, a \(84\)-dimensional matrix invariance algebra related to the \(8\)-component Dirac equation in the Foldy-Wouthuysen representation is deduced, from which the symmetry of the Dirac equation in the usual representation is recovered. Although not the principal purpose of the paper, the authors discuss a potential extension of the method to the Lie algebras \(\mathrm{SO}(n)\) and \(\mathrm{SO}(p,q)\) for arbitrary values of \(p+q=n\).
Reviewer: Rutwig Campoamor Stursberg (Madrid)Matrix factorizations, reality and Knörrer periodicityhttps://zbmath.org/1527.180102024-02-28T19:32:02.718555Z"Spellmann, Jan-Luca"https://zbmath.org/authors/?q=ai:spellmann.jan-luca"Young, Matthew B."https://zbmath.org/authors/?q=ai:young.matthew-bMotivated by periodicity theorems for real $K$-theory and Grothendieck-Witt theory, and, separatedly, work of \textit{K. Hori} and \textit{J. Walcher} [J. High Energy Phys. 2008, No. 4, Paper No. 030, 36 p. (2008; Zbl 1246.81337)] on the physics of Landau-Ginzburg orientifolds, this paper introduces and studies categories of real matrix factorizations. A fundamental property of matrix factorization categories is Knörrer periodicity [\textit{H. Knörrer}, Invent. Math. 88, 153--164 (1987; Zbl 0617.14033)], where
\begin{itemize}
\item $R=\mathbb{C}\left[\left[x_{1},\dots,x_{n}\right]\right]$;
\item $w\in R$ is a non-zero polynomial without a constant term;
\item A matrix factorization of $w$ is a $\mathbb{Z}/2\mathbb{Z}$-graded finite rank-free $R$-module $M$ with an odd $R$-linear endomorphism $d_{M}$ abiding $d_{M}^{2}=w\cdot\mathrm{id}_{M}$;
\item The 2-periodic differential graded (dg) category of matrix factorizations $\mathrm{MF}\left( R,w\right)$ and its triangulated homotopy category $\mathrm{HMF}\left( R,w\right)$ are categorical invariants of the singularity introduced by \textit{D. Eisenbud} [Trans. Am. Math. Soc. 260, 35--64 (1980; Zbl 0444.13006)] to study the homological algebra of $R/\left(w\right)$-modules.
\end{itemize}
Theorem.
There is a quasi-equivalence of dg categories
\[
\mathrm{MF}\left(R,w\right)\rightarrow\mathrm{MF}\left(R\left[\left[y,z\right]\right],w+y^{2}+z^{2}\right)
\]
Knörrer periodicity plays a significant role in the classification of hypersurface rings of finite maximal Cohen-Macaulay type [\textit{G. J. Leuschke} and \textit{R. Wiegand}, Cohen-Macaulay representations. Providence, RI: American Mathematical Society (AMS) (2012; Zbl 1252.13001); \textit{H. Knörrer}, Invent. Math. 88, 153--164 (1987; Zbl 0617.14033)], representing a basic quantum symmetry of Landau-Ginzburg models [\textit{K. Hori} and \textit{J. Walcher}, J. High Energy Phys. 2008, No. 4, Paper No. 030, 36 p. (2008; Zbl 1246.81337)].
The principal results in this paper are generalizations of Knörrer periodicity to categories of real matrix factorizations, which are structurally similar to $\left(1,1\right)$-periodicity for $KR$-theory and $4$-periodicity for Grothendieck-Witt theory. They are the following two theorems.
Theorem (Theorem 3.9). There is a quasi-equivalence of $\mathbb{R}$-linear dg categories
\[
\mathrm{Perf}\left(\mathrm{MF}_{\widehat{G}}\left(R,w\right)\right) \rightarrow\mathrm{Perf}\left(\mathrm{MF}_{\widehat{G}}\left(R\left[ \left[y,z\right]\right],w+y^{2}+z^{2}\right)\right)
\]
where
\begin{itemize}
\item $C_{2}$ is the multiplicative group $\left\{1,-1\right\}$;
\item $\pi:\widehat{G}\rightarrow C_{2}$ is a $c_2$-graded finite group with $G=\mathrm{ker\,}\pi$;
\item $\mathrm{Perf}\left(\mathcal{C}\right)$ is the triangulated hull of a dg category $\mathcal{C}$.
\end{itemize}
Theorem (Corollaries 5.13 and 5.14). There is a quasi-equivalence of $\mathbb{C}$-linear dg categories with duality
\[
\mathrm{Perf}\left(\mathrm{MF}_{G}\left(R,w\right)\right) \rightarrow\mathrm{Perf}\left(\mathrm{MF}_{G}\left(R\left[\left[ y,z\right]\right],w+y^{2}+z^{2}\right)\right)
\]
where the duality structure of the codomain is a shifted and signed version of that of the domain. In particular, there is a quasi-equivalence of $\mathbb{C}$-linear dg categories with duality
\[
\mathrm{Perf}\left(\mathrm{MF}_{G}\left(R,w\right)\right) \rightarrow\mathrm{Perf}\left(\mathrm{MF}_{G}\left(R\left[\left[y_{1},z_{1},y_{2},z_{2}\right]\right],w+y_{1}^{2}+z_{1}^{2}+y_{2}^{2}+z_{2}^{2}\right)\right)
\]
where both dg categories are given the same duality structure.
Reviewer: Hirokazu Nishimura (Tsukuba)Wedge domains in non-compactly causal symmetric spaceshttps://zbmath.org/1527.220222024-02-28T19:32:02.718555Z"Neeb, Karl-Hermann"https://zbmath.org/authors/?q=ai:neeb.karl-hermann"Ólafsson, Gestur"https://zbmath.org/authors/?q=ai:olafsson.gesturSummary: This article is part of an ongoing project aiming at the connections between causal structures on homogeneous spaces, Algebraic Quantum Field Theory, modular theory of operator algebras and unitary representations of Lie groups. In this article we concentrate on non-compactly causal symmetric spaces \(G/H\). This class contains de Sitter space but also other spaces with invariant partial ordering. The central ingredient is an Euler element \(h\) in the Lie algebra of \(\mathfrak{g} \). We define three different kinds of wedge domains depending on \(h\) and the causal structure on \(G/H\). Our main result is that the connected component containing the base point \(eH\) of these seemingly different domains all agree. Furthermore we discuss the connectedness of those wedge domains. We show that each of these spaces has a natural extension to a non-compactly causal symmetric space of the form \(G_{\mathbb{C}}/G^c\) where \(G^c\) is a certain real form of the complexification \(G_{\mathbb{C}}\) of \(G\). As \(G_{{\mathbb{C}}}/G^c\) is non-compactly causal, it also contains three types of wedge domains. Our results says that the intersection of these domains with \(G/H\) agree with the wedge domains in \(G/H\).\(\mathrm{SU}(N)\) polynomial integrals and some applicationshttps://zbmath.org/1527.280132024-02-28T19:32:02.718555Z"Borisenko, O."https://zbmath.org/authors/?q=ai:borysenko.olga-v|borisenko.oleg-fedorovich|borisenko.oleg-a|borisenko.oleksandr-andriyovych|borysenko.oleksandr-d"Voloshyn, S."https://zbmath.org/authors/?q=ai:voloshyn.s"Chelnokov, V."https://zbmath.org/authors/?q=ai:chelnokov.v-m|chelnokov.v-eSummary: We use the method of the Weingarten functions to evaluate \(\mathrm{SU}(N)\) integrals of the polynomial type. As an application we calculate various one-link integrals for lattice gauge and spin \(\mathrm{SU}(N)\) theories.Dirac operators for matrix algebras converging to coadjoint orbitshttps://zbmath.org/1527.460462024-02-28T19:32:02.718555Z"Rieffel, Marc A."https://zbmath.org/authors/?q=ai:rieffel.marc-aSummary: In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance. But physicists want even more to treat structures on spheres (and other spaces), such as vector bundles, Yang-Mills functionals, Dirac operators, etc., and they want to approximate these by corresponding structures on matrix algebras. In the present paper we provide a somewhat unified construction of Dirac operators on coadjoint orbits and on the matrix algebras that converge to them. This enables us to prove our main theorem, whose content is that, for the quantum metric-space structures determined by the Dirac operators that we construct, the matrix algebras do indeed converge to the coadjoint orbits, for a quite strong version of quantum Gromov-Hausdorff distance.Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomialshttps://zbmath.org/1527.530812024-02-28T19:32:02.718555Z"Ekholm, Tobias"https://zbmath.org/authors/?q=ai:ekholm.tobias"Ng, Lenhard"https://zbmath.org/authors/?q=ai:ng.lenhard-lSummary: We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large \(N\) duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We present an argument that the HOMFLY-PT wave function is determined from SFT by induction on Euler characteristic, and also show how to, more directly, extract its recursion relation by elimination theory applied to finitely many noncommutative equations. The latter can be viewed as the higher genus counterpart of the relation between the augmentation variety and Gromov-Witten disk potentials established in [ibid. 18, No. 4, 827--956 (2014; Zbl 1315.81076)] by \textit{M. Aganagic} et al., and, from this perspective, our results can be seen as an SFT approach to quantizing the augmentation variety.3-manifolds and Vafa-Witten theoryhttps://zbmath.org/1527.570152024-02-28T19:32:02.718555Z"Gukov, Sergei"https://zbmath.org/authors/?q=ai:gukov.sergei"Sheshmani, Artan"https://zbmath.org/authors/?q=ai:sheshmani.artan"Yau, Shing-Tung"https://zbmath.org/authors/?q=ai:yau.shing-tungSummary: We initiate explicit computations of Vafa-Witten invariants of 3-manifolds, analogous to Floer groups in the context of Donaldson theory. In particular, we explicitly compute the Vafa-Witten invariants of 3-manifolds in a family of concrete examples relevant to various surgery operations (the Gluck twist, knot surgeries, log-transforms). We also describe the structural properties that are expected to hold for general 3-manifolds, including the modular group action, relation to Floer homology, infinite-dimensionality for an arbitrary 3-manifold, and the absence of instantons.Entanglement in (4 + 1)-D-Dirac-type lattice model time-reversal-invarianthttps://zbmath.org/1527.810142024-02-28T19:32:02.718555Z"Lima, L. S."https://zbmath.org/authors/?q=ai:lima.leonardo-s|lima.lazaro-s|lima.lidiane-s-mSummary: Entanglement is studied in the neighborhood of topological phase transition in some topological insulators models as one-dimensional Rice-Mele model, two-dimensional Qi-Wu-Zhang model or Chern insulator and (4 + 1)-D higher dimensional Chern insulators. The systems describe electrons hopping in one, two or higher-dimensional chains respectively, being for the one-dimensional model, we have considered staggered hopping amplitudes. Our results show strong an effect of the variation of the topological charge \(Q\) in the neighborhood of topological phase transition on thermal entanglement for all cases analyzed.Anharmonic oscillator: a playground to get insight into renormalizationhttps://zbmath.org/1527.810592024-02-28T19:32:02.718555Z"Moghimi-Araghi, Saman"https://zbmath.org/authors/?q=ai:moghimi-araghi.saman"Loran, Farhang"https://zbmath.org/authors/?q=ai:loran.farhang(no abstract)A construction of quarter BPS coherent states and Brauer algebrashttps://zbmath.org/1527.810792024-02-28T19:32:02.718555Z"Lin, Hai"https://zbmath.org/authors/?q=ai:lin.hai.2|lin.hai|lin.hai.3|lin.hai.1"Zeng, Keyou"https://zbmath.org/authors/?q=ai:zeng.keyouSummary: BPS coherent states have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent states. Here we provide a construction of quarter BPS coherent states. They are coherent states built with two matrix fields, generalizing the half BPS case. These states are both the eigenstates of the annihilation operators and in the kernel of the anomalous dimension dilatation operator. Another useful labeling of quarter BPS states is by representations of Brauer algebras and their projection onto a subalgebra \(\mathbb{C}[S_n \times S_m]\). Here, the Schur-Weyl duality for the Brauer algebra plays an important role in organizing the operators. One interesting subclass of these Brauer states are labeled by representations involving two Young tableaux. We obtain the overlap between quarter BPS Brauer states and quarter BPS coherent states, where the Schur polynomials are used. We also derive superposition formulas transforming quarter BPS coherent states to quarter BPS Brauer states. The entanglement entropy of Brauer states as well as the overlap between Brauer states and squeezed states are also computed.High-order long-time approximation of \((N + 1)\)-level systems with near-resonance controlhttps://zbmath.org/1527.810862024-02-28T19:32:02.718555Z"Geng, Ru"https://zbmath.org/authors/?q=ai:geng.ru"Zu, Jian"https://zbmath.org/authors/?q=ai:zu.jian(no abstract)Cherenkov radiation with massive bosons and quantum frictionhttps://zbmath.org/1527.810922024-02-28T19:32:02.718555Z"Duerinckx, Mitia"https://zbmath.org/authors/?q=ai:duerinckx.mitia"Shirley, Christopher"https://zbmath.org/authors/?q=ai:shirley.christopherSummary: This work is devoted to several translation-invariant models in nonrelativistic quantum field theory (QFT), describing a nonrelativistic quantum particle interacting with a quantized relativistic field of bosons. In this setting, we aim at the rigorous study of Cherenkov radiation or friction effects at small disorder, which amounts to the metastability of the embedded mass shell of the bare nonrelativistic particle when the coupling to the quantized field is turned on. Although this problem is naturally approached by means of Mourre's celebrated commutator method, important regularity issues are known to be inherent to QFT models and restrict the application of the method. In this perspective, we introduce a novel non-standard procedure to construct Mourre conjugate operators, which differs from second quantization and allows to circumvent many regularity issues. To show its versatility, we apply this construction to the Nelson model with massive bosons, to Fröhlich's polaron model, and to a quantum friction model with massless bosons introduced by Bruneau and De Bièvre: for each of those examples, we improve on previous results.\(L_\infty\)-algebras of classical field theories and the Batalin-Vilkovisky formalismhttps://zbmath.org/1527.810932024-02-28T19:32:02.718555Z"Jurčo, Branislav"https://zbmath.org/authors/?q=ai:jurco.branislav"Raspollini, Lorenzo"https://zbmath.org/authors/?q=ai:raspollini.lorenzo"Sämann, Christian"https://zbmath.org/authors/?q=ai:samann.christian"Wolf, Martin"https://zbmath.org/authors/?q=ai:wolf.martinSummary: We review in detail the Batalin-Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory gives rise to an \(L_\infty\)-algebra and how quasi-isomorphisms between \(L_\infty\)-algebras correspond to classical equivalences of field theories. A few experts may be familiar with parts of our discussion, however, the material is presented from the perspective of a very general notion of a gauge theory. We also make a number of new observations and present some new results. Most importantly, we discuss in great detail higher (categorified) Chern-Simons theories and give some useful shortcuts in usually rather involved computations.
{\copyright} 2019 WILEY-VCH Verlag GmbH \& Co. KGaA, WeinheimMassive spin-2 field in arbitrary spacetimes -- the detailed derivationhttps://zbmath.org/1527.810942024-02-28T19:32:02.718555Z"Mazuet, Charles"https://zbmath.org/authors/?q=ai:mazuet.charles.2"Volkov, Mikhail S."https://zbmath.org/authors/?q=ai:volkov.mikhail-sSummary: We present the consistent theory of a free massive spin-2 field with 5 degrees of freedom propagating in spacetimes with an arbitrary geometry. We obtain this theory via linearizing the equations of the ghost-free massive gravity expressed in the tetrad formalism. The theory is parameterized by a \textit{non-symmetric} rank-2 tensor whose 16 components fulfill 11 constraints implied by the equations. When restricted to Einstein spaces, the theory reproduces the standard description of massive gravitons. In generic spacetimes, the theory does not show the massless limit and always propagates five degrees of freedom, even for the vanishing mass parameter. We illustrate these features by an explicit calculation for a homogeneous and isotropic cosmological background. It turns out that the spin-2 particles are always stable if they are sufficiently massive, hence they may be a part of the Dark Mater.Unifying lattice models, links and quantum geometric Langlands via branes in string theoryhttps://zbmath.org/1527.810952024-02-28T19:32:02.718555Z"Ashwinkumar, Meer"https://zbmath.org/authors/?q=ai:ashwinkumar.meer"Tan, Meng-Chwan"https://zbmath.org/authors/?q=ai:tan.meng-chwanSummary: We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Chern-Simons theory, (iii) the quantum geometric Langlands correspondence realized by Kapustin-Witten using 4d \(\mathcal{N}=4\) gauge theory and its quantum group modification, and (iv) the Gaitsgory-Lurie conjecture relating quantum groups/affine Kac-Moody algebras to Whittaker D-modules/W-algebras. This furnishes, purely physically via branes in string theory, a novel bridge between the mathematics of integrable systems, geometric topology, geometric representation theory, and quantum algebras.Axion from quivers in type II superstringshttps://zbmath.org/1527.810962024-02-28T19:32:02.718555Z"Belhaj, A."https://zbmath.org/authors/?q=ai:belhaj.adil"Douhou, K."https://zbmath.org/authors/?q=ai:douhou.karim"Ennadifi, S. E."https://zbmath.org/authors/?q=ai:ennadifi.salah-eddine"del Moral, M. P. Garcia"https://zbmath.org/authors/?q=ai:garcia-del-moral.maria-pilarSummary: We investigate a string-inspired axion extension of the standard model obtained from Type II superstrings using quiver method. In the first part, we discuss intersecting Type IIA D6-branes wrapping non trivial 3-cycles in the presence of the Peccei-Quinn symmetry \(\mathrm{U}(1)_{PQ}\). Concretely, a complex scalar field \(\phi = \rho\exp(\frac{i\sigma}{f_\sigma})\), where \(\sigma\) is a stringy axion generates a general fermion Yukawa coupling weighted by a flavor-dependent power \(n_f\) taking specific values. Using string theory and standard model data with adequate scales, we show that the corresponding axion window could lie in the allowed range \(10^9 \mathrm{GeV} \leq f_\sigma \leq 10^{12} \mathrm{GeV}\) matching with the recent cosmological results.
{\copyright} 2019 WILEY-VCH Verlag GmbH \& Co. KGaA, WeinheimRecounting special Lagrangian cycles in twistor families of \(K3\) surfaces (or: How I learned to stop worrying and count BPS states)https://zbmath.org/1527.810972024-02-28T19:32:02.718555Z"Kachru, Shamit"https://zbmath.org/authors/?q=ai:kachru.shamit"Tripathy, Arnav"https://zbmath.org/authors/?q=ai:tripathy.arnav"Zimet, Max"https://zbmath.org/authors/?q=ai:zimet.maxSummary: We consider asymptotics of certain BPS state counts in M-theory compactified on a \(K3\) surface. Our investigation is parallel to (and was inspired by) recent work in the mathematics literature by \textit{S. Filip} [``Counting special Lagrangian fibrations in twistor families of \(K3\) surfaces'', Preprint, \url{arXiv:1612.08684}, sell also Zbl 1451.14117], who studied the asymptotic count of special Lagrangian fibrations of a marked \(K3\) surface, with fibers of volume at most \(V_\ast\), in a generic twistor family of \(K3\) surfaces. We provide an alternate proof of Filip's results by adapting tools that Douglas and collaborators have used [\textit{M. R. Douglas}, ``The statistics of string/M theory vacua'', Preprint, \url{arXiv:0303194}; \textit{S. K. Ashok} and \textit{M. R. Douglas}, J. High Energy Phys. 2004, No. 1, 060, 36 p. (2004; Zbl 1243.83060); \textit{M. R. Douglas} et al., Commun. Math. Phys. 252, No. 1--3, 325--358 (2004; Zbl 1103.32011); \textit{F. Denef} and \textit{M. R. Douglas}, ``Distributions of flux vacua'', J. High Energy Phys. 2004, No. 5, Article No. 72, 46 p. (2004; \url{doi:10.1088/1126-6708/2004/05/072}); \textit{F. Denef} and \textit{M. R. Douglas}, ``Distributions of nonsupersymmetric flux vacua'', ibid. 2005, No. 3, Article No. 61, 30 p. (2005; \url{doi:10.1088/1126-6708/2005/03/061}); \textit{M. R. Douglas}, ``Random algebraic geometry, attractors and flux vacua'', in: Encyclopedia of Mathematical Physics. Amsterdam: Elsevier. 323--329 (2006)] to count flux vacua and attractor black holes. We similarly relate BPS state counts in 4d \(\mathcal{N} = 2\) supersymmetric gauge theories to certain counting problems in billiard dynamics and provide a simple proof of an old result in this field.Magnificent fourhttps://zbmath.org/1527.810982024-02-28T19:32:02.718555Z"Nekrasov, Nikita"https://zbmath.org/authors/?q=ai:nekrasov.nikita-aSummary: We present a statistical mechanical model whose random variables are solid partitions, \textit{i.e.}, Young diagrams built by stacking up four-dimensional hypercubes. Equivalently, it can be viewed as the model of random tessellations of \(\mathbf{R}^3\) by squashed cubes of four fixed orientations. The model computes the refined index of a system of \(D0\)-branes in the presence of \(D8\)-\(\overline{D8}\) system, with a \(B\)-field strong enough to support the bound states. Mathematically, it is the equivariant K-theoretic version of integration over the Hilbert scheme of points on \(\mathbb{C}^4\) and its higher rank analogues, albeit the definition is \textit{real}, not complex analytic. The model is a mother of all random partition models, including the equivariant Donaldson-Thomas theory and the four dimensional instanton counting. Finally, a version of our model with infinite solid partitions with four fixed plane partition asymptotics is the vertex contribution to the equivariant count of instantons on toric Calabi-Yau fourfolds.
The conjectured partition function of the model is presented. We have checked it up to six instantons (which is one step beyond the checks of the celebrated P. MacMahon's failed conjectures of the early twentieth century). A specialization of the formula is our earlier [``On the BPS/CFT correspondence'', Lecture at the University of Amsterdam string theory group Seminar, (2004)] conjecture on the equivariant K-theoretic Donaldson-Thomas theory, recently proven by \textit{A. Okounkov} [IAS/Park City Math. Ser. 24, 251--380 (2017; Zbl 1402.19001)].Holographic hadron masses in the language of quantum mechanicshttps://zbmath.org/1527.810992024-02-28T19:32:02.718555Z"Domokos, S. K."https://zbmath.org/authors/?q=ai:domokos.sophia-k"Bell, R."https://zbmath.org/authors/?q=ai:bell.robert-a|bell.robert-james|bell.rayna|bell.r-c|bell.robert-i|bell.ronald-p|bell.ralf|bell.renee|bell.robert-w|bell.rod-d|bell.robert-m|bell.rowen-b|bell.renelius"La, T."https://zbmath.org/authors/?q=ai:la.t"Mazza, P."https://zbmath.org/authors/?q=ai:mazza.paolo-p(no abstract)Equilibrium states for the massive sine-Gordon theory in the Lorentzian signaturehttps://zbmath.org/1527.811002024-02-28T19:32:02.718555Z"Bahns, Dorothea"https://zbmath.org/authors/?q=ai:bahns.dorothea"Pinamonti, Nicola"https://zbmath.org/authors/?q=ai:pinamonti.nicola"Rejzner, Kasia"https://zbmath.org/authors/?q=ai:rejzner.katarzynaSummary: In this paper we investigate the massive Sine-Gordon model in the ultraviolet finite regime in thermal states over the two-dimensional Minkowski spacetime. We combine recently developed methods of perturbative algebraic quantum field theory with techniques developed in the realm of constructive quantum field theory over Euclidean spacetimes to construct the correlation functions of the equilibrium state of the Sine-Gordon theory in the adiabatic limit. First of all, the observables of the Sine-Gordon theory are seen as functionals over the free configurations and are obtained as a suitable combination of the \(S\)-matrices of the interaction Lagrangian restricted to compact spacetime regions over the free massive theory. These \(S\)-matrices are given as power series in the coupling constant with values in the algebra of fields over the free massive theory. Adapting techniques like conditioning and inverse conditioning to spacetimes with Lorentzian signature, we prove that these power series converge when evaluated on a generic field configuration. The latter observation implies convergence in the strong operator topology in the GNS representations of the considered states. In the second part of the paper, adapting the cluster expansion technique to the Lorentzian case, we prove that the correlation functions of the interacting equilibrium state at finite temperature (KMS state) can be constructed also in the adiabatic limit, where the interaction Lagrangian is supported everywhere in space.Invertible phases of matter with spatial symmetryhttps://zbmath.org/1527.811012024-02-28T19:32:02.718555Z"Freed, Daniel S."https://zbmath.org/authors/?q=ai:freed.daniel-s"Hopkins, Michael J."https://zbmath.org/authors/?q=ai:hopkins.michael-jSummary: We propose a general formula for the group of invertible topological phases on a space \(Y\), possibly equipped with the action of a group \(G\). Our formula applies to arbitrary symmetry types. When \(Y\) is Euclidean space and \(G\) a crystallographic group, the term `topological crystalline phases' is sometimes used for these phases of matter.Anomaly cancellation in the topological stringhttps://zbmath.org/1527.811022024-02-28T19:32:02.718555Z"Costello, Kevin"https://zbmath.org/authors/?q=ai:costello.kevin-j"Li, Si"https://zbmath.org/authors/?q=ai:li.si.1Summary: We describe the coupling of holomorphic Chern-Simons theory at large \(N\) with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological \(B\)-model. At one loop this anomaly cancellation is analogous to the Green-Schwarz mechanism.
As an application, we introduce a type I version of Kodaira-Spencer theory in complex dimensions 3 and 5. In complex dimension 5, we show that it can only be coupled consistently at the quantum level to holomorphic Chern-Simons theory with gauge group \(SO(32)\). This is analogous to the Green-Schwarz mechanism for the physical type I string. This coupled system is conjectured to be a supersymmetric localization of type I string theory. In complex dimension 3, the required gauge group is \(SO(8)\).Unification of integrability in supersymmetric gauge theorieshttps://zbmath.org/1527.811032024-02-28T19:32:02.718555Z"Costello, Kevin"https://zbmath.org/authors/?q=ai:costello.kevin-j"Yagi, Junya"https://zbmath.org/authors/?q=ai:yagi.junyaSummary: A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six dimensions, topologically twisted and subjected to an \(\Omega\)-deformation. By realizing the six-dimensional theory in string theory and applying dualities, we unify various phenomena in which the eight-vertex model and the XYZ spin chain, as well as variants thereof, emerge from supersymmetric gauge theories.Modular factorization of superconformal indiceshttps://zbmath.org/1527.811042024-02-28T19:32:02.718555Z"Jejjala, Vishnu"https://zbmath.org/authors/?q=ai:jejjala.vishnu"Lei, Yang"https://zbmath.org/authors/?q=ai:lei.yang"van Leuven, Sam"https://zbmath.org/authors/?q=ai:van-leuven.sam"Li, Wei"https://zbmath.org/authors/?q=ai:li.wei.10Summary: Superconformal indices of four-dimensional \(\mathcal{N} = 1\) gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an \(\mathrm{SL}(3, \mathbb{Z})\) and \(\mathrm{SL}(2, \mathbb{Z})\ltimes \mathbb{Z}^2\) transformation. The former corresponds to a gluing transformation and the latter to an overall large diffeomorphism, both associated with a Heegaard splitting of the underlying geometry. The extension to more general transformations leads us to argue that a given index can be factorized in terms of a family of holomorphic blocks parametrized by modular (congruence sub)groups. We find precise agreement between this proposal and new modular properties of the elliptic \(\Gamma\) function. This leads to our conjecture for the ``modular factorization'' of superconformal lens indices of general \(\mathcal{N} = 1\) gauge theories. We provide evidence for the conjecture in the context of the free chiral multiplet and SQED and sketch the extension of our arguments to more general gauge theories. Assuming the validity of the conjecture, we systematically prove that a normalized part of superconformal lens indices defines a non-trivial first cohomology class associated with \(\mathrm{SL}(3, \mathbb{Z})\). Finally, we use this framework to propose a formula for the general lens space index.Hamiltonians for polaron models with subcritical ultraviolet singularitieshttps://zbmath.org/1527.811102024-02-28T19:32:02.718555Z"Lampart, Jonas"https://zbmath.org/authors/?q=ai:lampart.jonasSummary: We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity, we cover all subcritical (superrenormalisable) interactions. The Hamiltonian without cutoff is exhibited as an explicit self-adjoint operator obtained by a finite iteration procedure. The cutoff Hamiltonians converge to this operator in the strong resolvent sense after subtraction of a perturbative approximation for the ground-state energy.The Casimir effect in a dilute Bose gas at zero-temperature taking into account the contribution of self-energy within CJT theoryhttps://zbmath.org/1527.811202024-02-28T19:32:02.718555Z"Song, P. T."https://zbmath.org/authors/?q=ai:song.pham-the|song.pengtaoSummary: The Casimir effect in a weakly interacting Bose-Einstein condensate (BEC) gas is investigated at zero temperature within the Cornwall-Jackiw-Tomboulis (CJT) effective action approach under elastic and twisted boundary conditions (BCs) of the wave vector. After discussing the rationales for applying the CJT theory to a confinement BEC system, we establish the analytical formulae and then evaluate the numerical values of the Casimir force, which are essential for the observation experiment of the theoretical results.Casimir effect in a weakly interacting Bose gas confined by a parallel plate geometry in improved Hartree-Fock approximationhttps://zbmath.org/1527.820502024-02-28T19:32:02.718555Z"Thu, Nguyen Van"https://zbmath.org/authors/?q=ai:van-thu.nguyen"Song, Pham The"https://zbmath.org/authors/?q=ai:song.pham-theSummary: Within framework of the quantum field theory, in improved Hartree-Fock (IHF) approximation, the Casimir effect in a dilute single Bose-Einstein condensate (BEC) confined between two parallel plates is considered at zero temperature, in which the periodic and Dirichlet boundary conditions are employed. We find that the effective mass and order parameter of BEC strongly depend on distance separating two plates. Our results show that the effective mass, order parameter and the Casimir force in IHF approximation equal to their values in one-loop approximation added a corrected term due to contribution of two-loop diagrams.The parabolic-Gaussian potential and phonon effects on the polaron levels in alkali halogen ionic crystal quantum wellshttps://zbmath.org/1527.820592024-02-28T19:32:02.718555Z"Cui, Jian"https://zbmath.org/authors/?q=ai:cui.jian"Sun, Yong"https://zbmath.org/authors/?q=ai:sun.yong"Han, Shuang"https://zbmath.org/authors/?q=ai:han.shuang"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.254"An, Ran"https://zbmath.org/authors/?q=ai:an.ran"Ma, Xin-Jun"https://zbmath.org/authors/?q=ai:ma.xinjun"Li, Pei-Fang"https://zbmath.org/authors/?q=ai:li.peifang"Xiao, Jing-Lin"https://zbmath.org/authors/?q=ai:xiao.jinglinSummary: In this current study, we theoretically study how anisotropic parabolic potential affects polaron n excited state in strongly coupled polar crystals (KBr, KCl, RbCl) in asymmetric Gaussian potential quantum wells, through the combined approach of one unitary transformation and linear combination operator. In the restriction limit of strong coupling, we derive rigorous results for excited state energy. By using this combination method, polaron energy and electron energy are compared which energy both polaron and electron is affected by confined potential. In addition, the relationship between energy difference and coupling strength is also discussed. It is hoped that the theoretical results reveal a promising and importance of further study of polaron.Traversable wormholes in four dimensionshttps://zbmath.org/1527.830182024-02-28T19:32:02.718555Z"Maldacena, Juan"https://zbmath.org/authors/?q=ai:maldacena.juan-m.1"Milekhin, Alexey"https://zbmath.org/authors/?q=ai:milekhin.alexey"Popov, Fedor"https://zbmath.org/authors/?q=ai:popov.fedor-kSummary: We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does not lead to causality violations in the ambient space. It can be viewed as a pair of entangled near extremal black holes with an interaction term generated by the exchange of fermion fields. The solution can be embedded in the Standard Model by making its overall size small compared to the electroweak scale.Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortionhttps://zbmath.org/1527.830312024-02-28T19:32:02.718555Z"Zhang, Yang"https://zbmath.org/authors/?q=ai:zhang.yang.4"Wang, Bo"https://zbmath.org/authors/?q=ai:wang.bo.21|wang.bo.1|wang.boSummary: Adiabatic regularization is a method to remove UV divergences in quantum fields in curved spacetime. For relic gravitational wave generated during inflation, regularization on all \(k\)-modes of the power spectrum to 2nd adiabatic order, and of the energy density and pressure to 4th order, respectively, causes low-frequency distortions. To avoid these, we regularize only the short modes inside the horizon during inflation (corresponding to the present frequencies \(f \gtrsim 10^9\) Hz), and keep the long modes intact. Doing this does not violate the energy conservation since the \(k\)-modes of RGW are independent of each other during inflation. The resulting spectra are UV convergent and simultaneously free of low-frequency distortion, and these properties remain in the present spectra after evolution, in contrast to regularization at the present time which has some distortion or irregularities. The spectra generally exhibit quick oscillations in frequency domain, even if the initial spectra during inflation have no oscillations. This pattern is due to the interference between the positive and negative frequency modes developed during cosmic expansion, and may be probed by future RGW detections.A generic instability in clustering dark energy?https://zbmath.org/1527.830432024-02-28T19:32:02.718555Z"Hassani, Farbod"https://zbmath.org/authors/?q=ai:hassani.farbod"Adamek, Julian"https://zbmath.org/authors/?q=ai:adamek.julian"Kunz, Martin"https://zbmath.org/authors/?q=ai:kunz.martin"Shi, Pan"https://zbmath.org/authors/?q=ai:shi.pan"Wittwer, Peter"https://zbmath.org/authors/?q=ai:wittwer.peterSummary: In this paper, we study the effective field theory (EFT) of dark energy (DE) for the \(k\)-essence model beyond linear order. Using particle-mesh \(N\)-body simulations that consistently solve the DE evolution on a grid, we find that the next-to-leading order in the EFT expansion, which comprises the terms of the equations of motion that are quadratic in the field variables, gives rise to a generic instability in the regime of low speed of sound (high Mach number). We rule out the possibility of a numerical artefact by considering simplified cases in spherically and plane symmetric situations analytically. If the speed of sound vanishes exactly, the non-linear instability makes the evolution singular in finite time, signalling a breakdown of the EFT framework. The case of finite (but small) speed of sound is subtle, and the local singularity could be replaced by some other type of behaviour with strong non-linearities. While an ultraviolet completion may cure the problem in principle, there is no reason why this should be the case in general. As a result, for a large range of the effective speed of sound \(c_s\), a linear treatment is not adequate.On the global Casimir effect in the Schwarzschild spacetimehttps://zbmath.org/1527.830582024-02-28T19:32:02.718555Z"Muniz, C. R."https://zbmath.org/authors/?q=ai:muniz.celio-r"Tahim, M. O."https://zbmath.org/authors/?q=ai:tahim.makarius-o"Cunha, M. S."https://zbmath.org/authors/?q=ai:cunha.m-s"Vieira, H. S."https://zbmath.org/authors/?q=ai:vieira.h-sSummary: In this paper we study the vacuum quantum fluctuations of the stationary modes of an uncharged scalar field with mass \(m\) around a Schwarzschild black hole with mass \(M\), at zero and non-zero temperatures. The procedure consists of calculating the energy eigenvalues starting from the exact solutions found for the dynamics of the scalar field, considering a frequency cutoff in which the particle is not absorbed by the black hole. From this result, we obtain the exterior contributions for the vacuum energy associated to the stationary states of the scalar field, by considering the half-summing of the levels of energy and taking into account the respective degeneracies, in order to better capture the nontrivial topology of the black hole spacetime. Then we use the Riemann's zeta function to regularize the vacuum energy thus found. Such a regularized quantity is the Casimir energy, whose analytic computation we show to yield a convergent series. The Casimir energy obtained does not take into account any boundaries artificially imposed on the system, just the nontrivial spacetime topology associated to the source and its singularity. We suggest that this latter manifests itself through the vacuum tension calculated on the event horizon. We also investigate the problem by considering the thermal corrections via Helmholtz free energy calculation, computing the Casimir internal energy, the corresponding tension on the event horizon, the Casimir entropy, and the thermal capacity of the regularized quantum vacuum, analyzing their behavior at low and high temperatures, pointing out the thermodynamic instability of the system in the considered regime, i.e. \(mM \ll 1\).Mechanisms for primordial black hole production in string theoryhttps://zbmath.org/1527.830612024-02-28T19:32:02.718555Z"Özsoy, Ogan"https://zbmath.org/authors/?q=ai:ozsoy.ogan"Parameswaran, Susha"https://zbmath.org/authors/?q=ai:parameswaran.susha-l"Tasinato, Gianmassimo"https://zbmath.org/authors/?q=ai:tasinato.gianmassimo"Zavala, Ivonne"https://zbmath.org/authors/?q=ai:zavala.ivonneSummary: We consider mechanisms for producing a significant population of primordial black holes (PBHs) within string inspired single field models of inflation. The production of PBHs requires a large amplification in the power spectrum of curvature perturbations between scales associated with CMB and PBH formation. In principle, this can be achieved by temporarily breaking the slow-roll conditions during inflation. In this work, we identify two string setups that can realise this process. In string axion models of inflation, subleading non-perturbative effects can superimpose steep cliffs and gentle plateaus onto the leading axion potential. The cliffs can momentarily violate the slow-roll conditions, and the plateaus can lead to phases of ultra slow-roll inflation. We thus achieve a string motivated model which both matches the Planck observations at CMB scales and produces a population of light PBHs, which can account for an order one fraction of dark matter. In DBI models of inflation, a sharp increase in the speed of sound sourced by a steep downward step in the warp factor can drive the amplification. In this scenario, discovery of PBHs could indicate non-trivial dynamics in the bulk, such as flux-antibrane annihilation at the tip of a warped throat.JT gravity and the ensembles of random matrix theoryhttps://zbmath.org/1527.830712024-02-28T19:32:02.718555Z"Stanford, Douglas"https://zbmath.org/authors/?q=ai:stanford.douglas"Witten, Edward"https://zbmath.org/authors/?q=ai:witten.edwardSummary: We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer ``torsion.'' Presence of fermions in the boundary theory (and thus a symmetry \((-1)^\mathsf{F}\)) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.Open problems on classical de Sitter solutionshttps://zbmath.org/1527.830942024-02-28T19:32:02.718555Z"Andriot, David"https://zbmath.org/authors/?q=ai:andriot.davidSummary: Classical 10d string backgrounds with a 4d de Sitter space-time, \(D\)-brane and orientifold sources, are commonly believed to satisfy the following:
\begin{itemize}
\item[1.] \textit{There is no classical de Sitter solution with parallel sources}.
\item[2.] \textit{Classical de Sitter solutions with intersecting sources are unstable}.
\item[3.] \textit{Classical de Sitter solutions cannot have at the same time a large internal volume, a small string coupling, a bounded number of orientifolds and quantized fluxes}.
\end{itemize}
These three conjectures are of particular relevance to the swampland program, and if true, they challenge the connection of string theory to cosmology. We restrict here to a standard solution ansatz for which the problem is well-defined, and we still fail to prove analytically any of these conjectures. While developing new tools and obtaining new constraints, we identify remaining corners of parameter space where counter-examples to these conjectures could be found.
{\copyright} 2019 WILEY-VCH Verlag GmbH \& Co. KGaA, WeinheimThe swampland: introduction and reviewhttps://zbmath.org/1527.830962024-02-28T19:32:02.718555Z"Palti, Eran"https://zbmath.org/authors/?q=ai:palti.eranSummary: The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.
{\copyright} 2019 WILEY-VCH Verlag GmbH \& Co. KGaA, WeinheimQuasiclassical model of inhomogeneous cosmologyhttps://zbmath.org/1527.831102024-02-28T19:32:02.718555Z"Bojowald, Martin"https://zbmath.org/authors/?q=ai:bojowald.martin"Hancock, Freddy"https://zbmath.org/authors/?q=ai:hancock.freddySummary: Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-Universe cosmology, for instance in the state-dependent form of effective potentials. In addition, space-time properties are relevant in cosmology, in particular when combined with quantum corrections required to maintain general covariance in a consistent way. Here, an extension of previous investigations of static quasiclassical space-time models to dynamical ones is presented, describing the evolution of one-dimensional space as in the classical Lemaitre-Tolman-Bondi models. The corresponding spatial metric has two independent components, both of which are in general subject to quantum fluctuations. The main result is that individual moments from both components are indeed required for general covariance to be maintained at a semiclassical level, while quantum correlations between the components are less relevant.Arbitrary static, spherically symmetric space-times as solutions of scalar-tensor gravityhttps://zbmath.org/1527.831132024-02-28T19:32:02.718555Z"Bronnikov, K. A."https://zbmath.org/authors/?q=ai:bronnikov.kirill-a"Badalov, Kodir"https://zbmath.org/authors/?q=ai:badalov.kodir"Ibadov, Rustam"https://zbmath.org/authors/?q=ai:ibadov.rustamSummary: It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function \(f(\phi)\) and potential \(U(\phi)\). The scalar field in this representation can change its nature from canonical to phantom on certain coordinate spheres. This representation, however, is valid in general not in the full range of the radial coordinate but only piecewise. Two examples of STT representations are discussed: for the Reissner-Nordström metric and for the Simpson-Visser regularization of the Schwarzschild metric (the so-called black bounce space-time).Non-minimal gravitational reheating during kinationhttps://zbmath.org/1527.831212024-02-28T19:32:02.718555Z"Dimopoulos, Konstantinos"https://zbmath.org/authors/?q=ai:dimopoulos.konstantinos"Markkanen, Tommi"https://zbmath.org/authors/?q=ai:markkanen.tommiSummary: A new mechanism is presented which can reheat the Universe in non-oscillatory models of inflation, where the inflation period is followed by a period dominated by the kinetic density for the inflaton field (kination). The mechanism considers an auxiliary field non-minimally coupled to gravity. The auxiliary field is a spectator during inflation, rendered heavy by the non-minimal coupling to gravity. During kination however, the non-minimal coupling generates a tachyonic mass, which displaces the field, until its bare mass becomes important, leading to coherent oscillations. Then, the field decays into the radiation bath of the hot big bang. The model is generic and predictive, in that the resulting reheating temperature is a function only of the model parameters (masses and couplings) and not of initial conditions. It is shown that reheating can be very efficient also when considering only the Standard Model.Quantum computational complexity, Einstein's equations and accelerated expansion of the universehttps://zbmath.org/1527.831372024-02-28T19:32:02.718555Z"Ge, Xian-Hui"https://zbmath.org/authors/?q=ai:ge.xianhui"Wang, Bin"https://zbmath.org/authors/?q=ai:wang.bin.1Summary: We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.Consistency relations in multi-field inflationhttps://zbmath.org/1527.831392024-02-28T19:32:02.718555Z"Gong, Jinn-Ouk"https://zbmath.org/authors/?q=ai:gong.jinn-ouk"Seo, Min-Seok"https://zbmath.org/authors/?q=ai:seo.minseokSummary: We study the consequences of spatial coordinate transformation in multi-field inflation. Among the spontaneously broken de Sitter isometries, only dilatation in the comoving gauge preserves the form of the metric and thus results in quantum-protected Slavnov-Taylor identities. We derive the corresponding consistency relations between correlation functions of cosmological perturbations in two different ways, by the connected and one-particle-irreducible Green's functions. The lowest-order consistency relations are explicitly given, and we find that even in multi-field inflation the consistency relations in the soft limit are independent of the detail of the matter sector.Statistical nature of infrared dynamics on de Sitter backgroundhttps://zbmath.org/1527.831722024-02-28T19:32:02.718555Z"Tokuda, Junsei"https://zbmath.org/authors/?q=ai:tokuda.junsei"Tanaka, Takahiro"https://zbmath.org/authors/?q=ai:tanaka.takahiroSummary: In this study, we formulate a systematic way of deriving an effective equation of motion(EoM) for long wavelength modes of a massless scalar field with a general potential \(V(\phi)\) on de Sitter background, and investigate whether or not the effective EoM can be described as a classical stochastic process. Our formulation gives an extension of the usual stochastic formalism to including sub-leading secular growth coming from the nonlinearity of short wavelength modes. Applying our formalism to \(\lambda\phi^4\) theory, we explicitly derive an effective EoM which correctly recovers the next-to-leading secularly growing part at a late time, and show that this effective EoM can be seen as a classical stochastic process. Our extended stochastic formalism can describe all secularly growing terms which appear in all correlation functions with a specific operator ordering. The restriction of the operator ordering will not be a big drawback because the commutator of a light scalar field becomes negligible at large scales owing to the squeezing.Can all the infrared secular growth really be understood as increase of classical statistical variance?https://zbmath.org/1527.831732024-02-28T19:32:02.718555Z"Tokuda, Junsei"https://zbmath.org/authors/?q=ai:tokuda.junsei"Tanaka, Takahiro"https://zbmath.org/authors/?q=ai:tanaka.takahiroSummary: It is known that in the theory of light scalar fields during inflation, correlation functions suffer from infrared (IR) divergences or large IR loop corrections, leading to the breakdown of perturbation theory. In order to understand the physical meaning of such IR enhancement, we investigate the stochastic properties of an effective equation of motion (EoM) for long-wavelength modes of a canonically normalized light scalar field \(\phi\) with a general sufficiently flat interaction potential on de Sitter background. Firstly, we provide an alternative refined derivation of the effective action for long-wavelength modes which leads to the effective EoM that correctly reproduces all the IR correlation functions in a good approximation at a late time, by integrating out short-wavelength modes. Next, under the assumption that one can neglect non-local correlations in the influence functional exceeding the coarse-graining scale, we show that the effective EoM for IR modes of the ``average field'' in Schwinger-Keldysh formalism \(\phi_c^<\) can be interpreted as a classical stochastic process in the present model.