Recent zbMATH articles in MSC 81Thttps://zbmath.org/atom/cc/81T2021-04-16T16:22:00+00:00WerkzeugProposal for a conformal field theory interpretation of Watts' differential equation for percolation.https://zbmath.org/1456.824602021-04-16T16:22:00+00:00"Flohr, Michael"https://zbmath.org/authors/?q=ai:flohr.michael-a-i"Müller-Lohmann, Annekathrin"https://zbmath.org/authors/?q=ai:muller-lohmann.annekathrinThe full vertex functions constrained by the longitudinal and transverse Ward-Takahashi identities in massless \(\mathrm{QED_3}\) theory.https://zbmath.org/1456.813122021-04-16T16:22:00+00:00"Yu, Yang"https://zbmath.org/authors/?q=ai:yu.yang"Li, Jian-Feng"https://zbmath.org/authors/?q=ai:li.jianfengThe averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality.https://zbmath.org/1456.830342021-04-16T16:22:00+00:00"Iizuka, Norihiro"https://zbmath.org/authors/?q=ai:iizuka.norihiro"Ishibashi, Akihiro"https://zbmath.org/authors/?q=ai:ishibashi.akihiro"Maeda, Kengo"https://zbmath.org/authors/?q=ai:maeda.kengoSummary: We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated than the odd-dimensional case. In two-dimensions, we derive the ANEC by applying the no-bulk-shortcut principle. In four-dimensions, we derive an inequality which essentially provides the lower-bound for the ANEC with a weight function. For this purpose, and also to get some geometric insights into gravitational conformal anomalies, we express the stress-energy formulas in terms of geometric quantities such as the expansions of boundary null geodesics and a quasi-local mass of the boundary geometry. We argue when the lowest bound is achieved and also discuss when the averaged value of the null energy can be negative, considering a simple example of a spatially compact universe with wormhole throat.Confronting dual models of the strong interaction.https://zbmath.org/1456.813382021-04-16T16:22:00+00:00"Ridkokasha, I."https://zbmath.org/authors/?q=ai:ridkokasha.iBosonic representation of spin operators in the field-induced critical phase of spin-1 Haldane chains.https://zbmath.org/1456.821822021-04-16T16:22:00+00:00"Sato, Masahiro"https://zbmath.org/authors/?q=ai:sato.masahiroCFT in AdS and boundary RG flows.https://zbmath.org/1456.813792021-04-16T16:22:00+00:00"Giombi, Simone"https://zbmath.org/authors/?q=ai:giombi.simone"Khanchandani, Himanshu"https://zbmath.org/authors/?q=ai:khanchandani.himanshuSummary: Using the fact that flat space with a boundary is related by a Weyl transformation to Anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large \(N\) critical \(O(N)\) model in general dimension \(d\), as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured \(F\)-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.Conformal field theory out of equilibrium: a review.https://zbmath.org/1456.813512021-04-16T16:22:00+00:00"Bernard, Denis"https://zbmath.org/authors/?q=ai:bernard.denis"Doyon, Benjamin"https://zbmath.org/authors/?q=ai:doyon.benjaminFinite-temperature form factors in the free Majorana theory.https://zbmath.org/1456.821202021-04-16T16:22:00+00:00"Doyon, Benjamin"https://zbmath.org/authors/?q=ai:doyon.benjaminGravitational duals to the grand canonical ensemble abhor Cauchy horizons.https://zbmath.org/1456.830802021-04-16T16:22:00+00:00"Hartnoll, Sean A."https://zbmath.org/authors/?q=ai:hartnoll.sean-a"Horowitz, Gary T."https://zbmath.org/authors/?q=ai:horowitz.gary-t"Kruthoff, Jorrit"https://zbmath.org/authors/?q=ai:kruthoff.jorrit"Santos, Jorge E."https://zbmath.org/authors/?q=ai:santos.jorge-eSummary: The gravitational dual to the grand canonical ensemble of a large \(N\) holographic theory is a charged black hole. These spacetimes -- for example Reissner-Nordström-AdS -- can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.Multicritical behaviour in the fully frustrated \textit{XY} model and related systems.https://zbmath.org/1456.821382021-04-16T16:22:00+00:00"Hasenbusch, Martin"https://zbmath.org/authors/?q=ai:hasenbusch.martin"Pelissetto, Andrea"https://zbmath.org/authors/?q=ai:pelissetto.andrea"Vicari, Ettore"https://zbmath.org/authors/?q=ai:vicari.ettoreOn single-copy entanglement.https://zbmath.org/1456.813132021-04-16T16:22:00+00:00"Peschel, Ingo"https://zbmath.org/authors/?q=ai:peschel.ingo"Zhao, Jize"https://zbmath.org/authors/?q=ai:zhao.jizeConstructive renormalization of the 2-dimensional Grosse-Wulkenhaar model.https://zbmath.org/1456.813062021-04-16T16:22:00+00:00"Wang, Zhituo"https://zbmath.org/authors/?q=ai:wang.zhituoSummary: We study a quartic matrix model with partition function \(Z=\int d\;M\exp \mathrm{Tr}\;(-\Delta M^2-\frac{\lambda }{4}M^4)\). The integral is over the space of Hermitian \((\varLambda +1)\times (\varLambda +1)\) matrices, the matrix \(\Delta \), which is not a multiple of the identity matrix, encodes the dynamics and \(\lambda >0\) is a scalar coupling constant. We proved that the logarithm of the partition function is the Borel sum of the perturbation series and hence is a well-defined analytic function of the coupling constant in certain analytic domain of \(\lambda \), by using the multi-scale loop vertex expansions. All the non-planar graphs generated in the perturbation expansions have been taken care of on the same footing as the planar ones. This model is derived from the self-dual \(\phi ^4\) theory on the 2-dimensional Moyal space also called the 2-dimensional Grosse-Wulkenhaar model. This would also be the first fully constructed matrix model which is non-trivial and not solvable.Models for the BPS Berry connection.https://zbmath.org/1456.812082021-04-16T16:22:00+00:00"Ohya, Satoshi"https://zbmath.org/authors/?q=ai:ohya.satoshiConformal invariance and its breaking in a stochastic model of a fluctuating interface.https://zbmath.org/1456.823312021-04-16T16:22:00+00:00"Alcaraz, Francisco C."https://zbmath.org/authors/?q=ai:alcaraz.francisco-castilho"Levine, Erel"https://zbmath.org/authors/?q=ai:levine.erel"Rittenberg, Vladimir"https://zbmath.org/authors/?q=ai:rittenberg.vladimirZeno and anti-Zeno effects in a dissipative quantum Brownian oscillator model.https://zbmath.org/1456.812992021-04-16T16:22:00+00:00"Bandyopadhyay, Malay"https://zbmath.org/authors/?q=ai:bandyopadhyay.malayDyonic objects and tensor network representation.https://zbmath.org/1456.813312021-04-16T16:22:00+00:00"Belhaj, A."https://zbmath.org/authors/?q=ai:belhaj.adil"El Maadi, Y."https://zbmath.org/authors/?q=ai:el-maadi.y"Ennadifi, S-E."https://zbmath.org/authors/?q=ai:ennadifi.salah-eddine"Hassouni, Y."https://zbmath.org/authors/?q=ai:hassouni.yassine"Sedra, M. B."https://zbmath.org/authors/?q=ai:sedra.moulay-brahimOff-critical logarithmic minimal models.https://zbmath.org/1456.813972021-04-16T16:22:00+00:00"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Seaton, Katherine A."https://zbmath.org/authors/?q=ai:seaton.katherine-aThe \(\Lambda- \mathrm{BMS}_4\) charge algebra.https://zbmath.org/1456.812152021-04-16T16:22:00+00:00"Compère, Geoffrey"https://zbmath.org/authors/?q=ai:compere.geoffrey"Fiorucci, Adrien"https://zbmath.org/authors/?q=ai:fiorucci.adrien"Ruzziconi, Romain"https://zbmath.org/authors/?q=ai:ruzziconi.romainSummary: The surface charge algebra of generic asymptotically locally \(\mathrm{(A)dS}_4\) spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The \(\Lambda- \mathrm{BMS}_4\) charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the \(\mathrm{BMS}_4\) charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The \(\mathrm{BMS}_4\) surface charges represent the \(\mathrm{BMS}_4\) algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the \(\mathrm{BMS}_4\) flux algebra admits no non-trivial central extension.A one parameter family of Calabi-Yau manifolds with attractor points of rank two.https://zbmath.org/1456.830892021-04-16T16:22:00+00:00"Candelas, Philip"https://zbmath.org/authors/?q=ai:candelas.philip"de la Ossa, Xenia"https://zbmath.org/authors/?q=ai:de-la-ossa.xenia-c"Elmi, Mohamed"https://zbmath.org/authors/?q=ai:elmi.mohamed"van Straten, Duco"https://zbmath.org/authors/?q=ai:van-straten.ducoSummary: In the process of studying the \(\zeta\)-function for one parameter families of Calabi-Yau manifolds we have been led to a manifold, first studied by Verrill, for which the quartic numerator of the \(\zeta\)-function factorises into two quadrics remarkably often. Among these factorisations, we find \textit{persistent factorisations}; these are determined by a parameter that satisfies an algebraic equation with coefficients in \(\mathbb{Q}\), so independent of any particular prime. Such factorisations are expected to be modular with each quadratic factor associated to a modular form. If the parameter is defined over \(\mathbb{Q}\) this modularity is assured by the proof of the Serre Conjecture. We identify three values of the parameter that give rise to persistent factorisations, one of which is defined over \(\mathbb{Q}\), and identify, for all three cases, the associated modular groups. We note that these factorisations are due a splitting of Hodge structure and that these special values of the parameter are rank two attractor points in the sense of IIB supergravity. To our knowledge, these points provide the first explicit examples of non-singular, non-rigid rank two attractor points for Calabi-Yau manifolds of full SU(3) holonomy. The values of the periods and their covariant derivatives, at the attractor points, are identified in terms of critical values of the \(L\)-functions of the modular groups. Thus the critical \(L\)-values enter into the calculation of physical quantities such as the area of the black hole in the 4D spacetime. In our search for additional rank two attractor points, we perform a statistical analysis of the numerator of the \(\zeta\)-function and are led to conjecture that the coefficients in this polynomial are distributed according to the statistics of random USp(4) matrices.On conservation laws, relaxation and pre-relaxation after a quantum quench.https://zbmath.org/1456.812322021-04-16T16:22:00+00:00"Fagotti, Maurizio"https://zbmath.org/authors/?q=ai:fagotti.maurizioGLSMs for exotic Grassmannians.https://zbmath.org/1456.814342021-04-16T16:22:00+00:00"Gu, Wei"https://zbmath.org/authors/?q=ai:gu.wei"Sharpe, Eric"https://zbmath.org/authors/?q=ai:sharpe.eric-r"Zou, Hao"https://zbmath.org/authors/?q=ai:zou.haoSummary: In this paper we explore nonabelian gauged linear sigma models (GLSMs) for symplectic and orthogonal Grassmannians and flag manifolds, checking e.g. global symmetries, Witten indices, and Calabi-Yau conditions, following up a proposal in the math community. For symplectic Grassmannians, we check that Coulomb branch vacua of the GLSM are consistent with ordinary and equivariant quantum cohomology of the space.Perturbative linearization of supersymmetric Yang-Mills theory.https://zbmath.org/1456.814182021-04-16T16:22:00+00:00"Ananth, Sudarshan"https://zbmath.org/authors/?q=ai:ananth.sudarshan"Lechtenfeld, Olaf"https://zbmath.org/authors/?q=ai:lechtenfeld.olaf"Malcha, Hannes"https://zbmath.org/authors/?q=ai:malcha.hannes"Nicolai, Hermann"https://zbmath.org/authors/?q=ai:nicolai.hermann"Pandey, Chetan"https://zbmath.org/authors/?q=ai:pandey.chetan"Pant, Saurabh"https://zbmath.org/authors/?q=ai:pant.saurabhSummary: Supersymmetric gauge theories are characterized by the existence of a transformation of the bosonic fields (Nicolai map) such that the Jacobi determinant of the transformation equals the product of the Matthews-Salam-Seiler and Faddeev-Popov determinants. This transformation had been worked out to second order in the coupling constant. In this paper, we extend this result (and the framework itself ) to third order in the coupling constant. A diagrammatic approach in terms of tree diagrams, aiming to extend this map to arbitrary orders, is outlined. This formalism bypasses entirely the use of anti-commuting variables, as well as issues concerning the (non-)existence of off-shell formulations for these theories. It thus offers a fresh perspective on supersymmetric gauge theories and, in particular, the ubiquitous \(\mathcal{N} = 4\) theory.Renormalization of Galilean electrodynamics.https://zbmath.org/1456.813102021-04-16T16:22:00+00:00"Chapman, Shira"https://zbmath.org/authors/?q=ai:chapman.shira"Di Pietro, Lorenzo"https://zbmath.org/authors/?q=ai:di-pietro.lorenzo"Grosvenor, Kevin T."https://zbmath.org/authors/?q=ai:grosvenor.kevin-t"Yan, Ziqi"https://zbmath.org/authors/?q=ai:yan.ziqiSummary: We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schrödinger scalar in 2+1 dimensions. At the classical level, the theory with minimal coupling is obtained from a null-reduction of relativistic Maxwell theory coupled to a complex scalar field in 3+1 dimensions and is closely related to the Galilean electromagnetism of Le-Bellac and Lévy-Leblond. Due to the presence of a dimensionless, gauge-invariant scalar field in the Galilean multiplet of the gauge-field, we find that at the quantum level an infinite number of couplings is generated. We explain how to handle the quantum corrections systematically using the background field method. Due to a non-renormalization theorem, the beta function of the gauge coupling is found to vanish to all orders in perturbation theory, leading to a continuous family of fixed points where the non-relativistic conformal symmetry is preserved.Metric algebroid and Dirac generating operator in Double Field Theory.https://zbmath.org/1456.830902021-04-16T16:22:00+00:00"Carow-Watamura, Ursula"https://zbmath.org/authors/?q=ai:carow-watamura.ursula"Miura, Kohei"https://zbmath.org/authors/?q=ai:miura.kohei"Watamura, Satoshi"https://zbmath.org/authors/?q=ai:watamura.satoshi"Yano, Taro"https://zbmath.org/authors/?q=ai:yano.taroSummary: We give a formulation of Double Field Theory (DFT) based on a metric algebroid. We derive a covariant completion of the Bianchi identities, i.e. the pre-Bianchi identity in torsion and an improved generalized curvature, and the pre-Bianchi identity including the dilaton contribution. The derived bracket formulation by the Dirac generating operator is applied to the metric algebroid. We propose a generalized Lichnerowicz formula and show that it is equivalent to the pre-Bianchi identities. The dilaton in this setting is included as an ambiguity in the divergence. The projected generalized Lichnerowicz formula gives a new formulation of the DFT action. The closure of the generalized Lie derivative on the spin bundle yields the Bianchi identities as a consistency condition. A relation to the generalized supergravity equations (GSE) is discussed.Dressing bulk fields in \(\mathrm{AdS}_3\).https://zbmath.org/1456.830272021-04-16T16:22:00+00:00"Kabat, Daniel"https://zbmath.org/authors/?q=ai:kabat.daniel"Lifschytz, Gilad"https://zbmath.org/authors/?q=ai:lifschytz.giladSummary: We study a set of CFT operators suitable for reconstructing a charged bulk scalar field \(\varphi\) in \(\mathrm{AdS}_3\) (dual to an operator \(\mathcal{O}\) of dimension \(\Delta\) in the CFT) in the presence of a conserved spin-\(n\) current in the CFT. One has to sum a tower of smeared non-primary scalars \({\partial}_+^m{J}^{(m)}\), where \(J^{(m)}\) are primaries with twist \(\Delta\) and spin \(m\) built from \(\mathcal{O}\) and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order \(1/N\) this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line.Multi-Regge limit of the two-loop five-point amplitudes in \(\mathcal{N} = 4\) super Yang-Mills and \(\mathcal{N} = 8\) supergravity.https://zbmath.org/1456.831122021-04-16T16:22:00+00:00"Caron-Huot, Simon"https://zbmath.org/authors/?q=ai:caron-huot.simon"Chicherin, Dmitry"https://zbmath.org/authors/?q=ai:chicherin.dmitry"Henn, Johannes"https://zbmath.org/authors/?q=ai:henn.johannes-m"Zhang, Yang"https://zbmath.org/authors/?q=ai:zhang.yang"Zoia, Simone"https://zbmath.org/authors/?q=ai:zoia.simoneSummary: In previous work [\textit{E. D'Hoker} et al.,ibid. 2020, No. 8, Paper No. 135, 80 p. (2020; Zbl 1454.83159); \textit{C. R. Mafra} and \textit{O. Schlotterer}, ibid. 2015, No. 10, Paper No. 124, 29 p. (2015; Zbl 1388.83860)], the two-loop five-point amplitudes in \(\mathcal{N} = 4\) super Yang-Mills theory and \(\mathcal{N} = 8\) supergravity were computed at symbol level. In this paper, we compute the full functional form. The amplitudes are assembled and simplified using the analytic expressions of the two-loop pentagon integrals in the physical scattering region. We provide the explicit functional expressions, and a numerical reference point in the scattering region. We then calculate the multi-Regge limit of both amplitudes. The result is written in terms of an explicit transcendental function basis. For certain non-planar colour structures of the \(\mathcal{N} = 4\) super Yang-Mills amplitude, we perform an independent calculation based on the BFKL effective theory. We find perfect agreement. We comment on the analytic properties of the amplitudes.Averaging over Narain moduli space.https://zbmath.org/1456.830672021-04-16T16:22:00+00:00"Maloney, Alexander"https://zbmath.org/authors/?q=ai:maloney.alexander"Witten, Edward"https://zbmath.org/authors/?q=ai:witten.edwardSummary: Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT's to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain's family of two-dimensional CFT's obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like \(\mathrm{U}(1)^{2D}\) Chern-Simons theory than like Einstein gravity.A counterexample to the Nelson-Seiberg theorem.https://zbmath.org/1456.814442021-04-16T16:22:00+00:00"Sun, Zheng"https://zbmath.org/authors/?q=ai:sun.zheng"Tan, Zipeng"https://zbmath.org/authors/?q=ai:tan.zipeng"Yang, Lu"https://zbmath.org/authors/?q=ai:yang.luSummary: We present a counterexample to the Nelson-Seiberg theorem and its extensions. The model has 4 chiral fields, including one R-charge 2 field and no R-charge 0 filed. Giving generic values of coefficients in the renormalizable superpotential, there is a supersymmetric vacuum with one complex dimensional degeneracy. The superpotential equals zero and the R-symmetry is broken everywhere on the degenerated vacuum. The existence of such a vacuum disagrees with both the original Nelson-Seiberg theorem and its extensions, and can be viewed as the consequence of a non-generic R-charge assignment. Such counterexamples may introduce error to the field counting method for surveying the string landscape, and are worth further investigations.A nilpotency index of conformal manifolds.https://zbmath.org/1456.814362021-04-16T16:22:00+00:00"Komargodski, Zohar"https://zbmath.org/authors/?q=ai:komargodski.zohar"Razamat, Shlomo S."https://zbmath.org/authors/?q=ai:razamat.shlomo-s"Sela, Orr"https://zbmath.org/authors/?q=ai:sela.orr"Sharon, Adar"https://zbmath.org/authors/?q=ai:sharon.adarSummary: We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.Correction to: ``Ising model: local spin correlations and conformal invariance''.https://zbmath.org/1456.821342021-04-16T16:22:00+00:00"Gheissari, Reza"https://zbmath.org/authors/?q=ai:gheissari.reza"Hongler, Clément"https://zbmath.org/authors/?q=ai:hongler.clement"Park, S. C."https://zbmath.org/authors/?q=ai:park.soon-chull|park.shin-chul|park.su-chan|park.sojung-carol|park.sang-chan|park.seong-chan|park.soon-cheolCorrects the license of the authors' paper [ibid. 367, No. 3, 771--833 (2019; Zbl 1419.82012)].Subleading corrections to the free energy in a theory with \(N^{5/3}\) scaling.https://zbmath.org/1456.814392021-04-16T16:22:00+00:00"Liu, James T."https://zbmath.org/authors/?q=ai:liu.james-t"Lu, Yifan"https://zbmath.org/authors/?q=ai:lu.yifanSummary: We numerically investigate the sphere partition function of a Chern-Simons-matter theory with \(\mathrm{SU} (N)\) gauge group at level \(k\) coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order \(N^{5/3}\) behavior of the free energy, we find numerical evidence for a term of the form \((2/9) \log N\). We conjecture that this term may be universal in theories with \(N^{5/3}\) scaling in the large-\(N\) limit with the Chern-Simons level \(k\) held fixed.Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs.https://zbmath.org/1456.813702021-04-16T16:22:00+00:00"Doyon, Benjamin"https://zbmath.org/authors/?q=ai:doyon.benjamin"Hoogeveen, Marianne"https://zbmath.org/authors/?q=ai:hoogeveen.marianne"Bernard, Denis"https://zbmath.org/authors/?q=ai:bernard.denisFermi gas approach to general rank theories and quantum curves.https://zbmath.org/1456.813432021-04-16T16:22:00+00:00"Kubo, Naotaka"https://zbmath.org/authors/?q=ai:kubo.naotakaSummary: It is known that matrix models computing the partition functions of three-dimensional \(\mathcal{N} = 4\) superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.Aspects of the \(s\) transformation bootstrap.https://zbmath.org/1456.813552021-04-16T16:22:00+00:00"Brehm, Enrico M."https://zbmath.org/authors/?q=ai:brehm.enrico-m"Das, Diptarka"https://zbmath.org/authors/?q=ai:das.diptarkaGauged sigma-models with nonclosed 3-form and twisted Jacobi structures.https://zbmath.org/1456.814062021-04-16T16:22:00+00:00"Chatzistavrakidis, Athanasios"https://zbmath.org/authors/?q=ai:chatzistavrakidis.athanasios"Šimunić, Grgur"https://zbmath.org/authors/?q=ai:simunic.grgurSummary: We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.A Monte Carlo approach to the worldline formalism in curved space.https://zbmath.org/1456.812942021-04-16T16:22:00+00:00"Corradini, Olindo"https://zbmath.org/authors/?q=ai:corradini.olindo"Muratori, Maurizio"https://zbmath.org/authors/?q=ai:muratori.maurizioSummary: We present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as \textit{YLOOPS} with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time of the associated bosonic point-particle, hence such procedure may be seen as an analogue of the time-slicing (TS) discretization already introduced to construct quantum path integrals in curved space. As a result, a TS counter-term is taken into account during the computation. The method is tested against existing analytic calculations of the heat kernel for a free bosonic point-particle in a \(D\)-dimensional maximally symmetric space.Superconformal RG interfaces in holography.https://zbmath.org/1456.814202021-04-16T16:22:00+00:00"Arav, Igal"https://zbmath.org/authors/?q=ai:arav.igal"Cheung, K. C. Matthew"https://zbmath.org/authors/?q=ai:cheung.k-c-matthew"Gauntlett, Jerome P."https://zbmath.org/authors/?q=ai:gauntlett.jerome-p"Roberts, Matthew M."https://zbmath.org/authors/?q=ai:roberts.matthew-m"Rosen, Christopher"https://zbmath.org/authors/?q=ai:rosen.christopherSummary: We construct gravitational solutions that holographically describe two different \(d = 4\) SCFTs joined together at a co-dimension one, planar RG interface and preserving \(d = 3\) superconformal symmetry. The RG interface joins \(\mathcal{N} = 4\) SYM theory on one side with the \(\mathcal{N} = 1\) Leigh-Strassler SCFT on the other. We construct a family of such solutions, which in general are associated with spatially dependent mass deformations on the \(\mathcal{N} = 4\) SYM side, but there is a particular solution for which these deformations vanish. We also construct a Janus solution with the Leigh-Strassler SCFT on either side of the interface. Gravitational solutions associated with superconformal interfaces involving ABJM theory and two \(d = 3 \ \mathcal{N} = 1\) SCFTs with \(G_2\) symmetry are also discussed and shown to have similar properties, but they also exhibit some new features.Generalized planar Feynman diagrams: collections.https://zbmath.org/1456.813192021-04-16T16:22:00+00:00"Borges, Francisco"https://zbmath.org/authors/?q=ai:borges.francisco"Cachazo, Freddy"https://zbmath.org/authors/?q=ai:cachazo.freddySummary: Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each degeneration of a tree leads to a single planar neighbor. Amplitudes are computed as an integral over the space of metrics where edge lengths are Schwinger parameters. In this work we propose that a natural generalization of Feynman diagrams is provided by what are known as metric tree arrangements. These are collections of metric trees subject to a compatibility condition on the metrics. We introduce the notion of \textit{planar col lections of Feynman diagrams} and argue that using planarity one can generate all planar collections starting from any one. Moreover, we identify a canonical initial collection for all \(n\). Generalized \(k = 3\) biadjoint amplitudes, introduced by Early, Guevara, Mizera, and one of the authors, are easily computed as an integral over the space of metrics of planar collections of Feynman diagrams.\(\mathcal{N} = 1\) supersymmetric double field theory and the generalized Kerr-Schild ansatz.https://zbmath.org/1456.830072021-04-16T16:22:00+00:00"Lescano, Eric"https://zbmath.org/authors/?q=ai:lescano.eric"Rodríguez, Jesús A."https://zbmath.org/authors/?q=ai:rodriguez.jesus-aSummary: We construct the \(\mathcal{N} = 1\) supersymmetric extension of the generalized Kerr-Schild ansatz in the flux formulation of Double Field Theory. We show that this ansatz is compatible with \(\mathcal{N} = 1\) supersymmetry as long as it is not written in terms of generalized null vectors. Supersymmetric consistency is obtained through a set of conditions that imply linearity of the generalized gravitino perturbation and unrestricted perturbations of the generalized background dilaton and dilatino. As a final step we parametrize the previous theory in terms of the field content of the low energy effective 10-dimensional heterotic supergravity and we find that the perturbation of the 10-dimensional vielbein, Kalb-Ramond field, gauge field, gravitino and gaugino can be written in terms of vectors, as expected.A string theory realization of special unitary quivers in 3 dimensions.https://zbmath.org/1456.830942021-04-16T16:22:00+00:00"Collinucci, Andrés"https://zbmath.org/authors/?q=ai:collinucci.andres"Valandro, Roberto"https://zbmath.org/authors/?q=ai:valandro.robertoSummary: We propose a string theory realization of three-dimensional \(\mathcal{N} = 4\) quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3's, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a \(T^3\). The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs.Spatially modulated and supersymmetric mass deformations of \(\mathcal{N} = 4\) SYM.https://zbmath.org/1456.831102021-04-16T16:22:00+00:00"Arav, Igal"https://zbmath.org/authors/?q=ai:arav.igal"Cheung, K. C. Matthew"https://zbmath.org/authors/?q=ai:cheung.k-c-matthew"Gauntlett, Jerome P."https://zbmath.org/authors/?q=ai:gauntlett.jerome-p"Roberts, Matthew M."https://zbmath.org/authors/?q=ai:roberts.matthew-m"Rosen, Christopher"https://zbmath.org/authors/?q=ai:rosen.christopherSummary: We study mass deformations of \(\mathcal{N} = 4, \ d = 4\) SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of \(\mathcal{N} = 1^\ast\) theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve \(d = 3\) conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using \(D = 5\) theories of gravity that arise from consistent truncations of SO(6) gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve \(d = 3\) superconformal symmetry we construct a rich set of Janus solutions of \(\mathcal{N} = 4\) SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with \(\mathcal{N} = 4\) SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric \( \mathrm{AdS}_4 \times S^1 \times S^5\) solution of type IIB supergravity.\(\mathcal{N} = 2\) dualities and \(Z\)-extremization in three dimensions.https://zbmath.org/1456.814452021-04-16T16:22:00+00:00"Willett, Brian"https://zbmath.org/authors/?q=ai:willett.brian"Yaakov, Itamar"https://zbmath.org/authors/?q=ai:yaakov.itamarSummary: We use localization techniques to study duality in \(\mathcal{N} = 2\) supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.Systematic effective field theory analysis of the \(d=2+1\) quantum XY model at low temperatures.https://zbmath.org/1456.813852021-04-16T16:22:00+00:00"Hofmann, Christoph P."https://zbmath.org/authors/?q=ai:hofmann.christoph-pThe large-\(N\) limit of the 4d \(\mathcal{N} = 1\) superconformal index.https://zbmath.org/1456.814212021-04-16T16:22:00+00:00"Cabo-Bizet, Alejandro"https://zbmath.org/authors/?q=ai:cabo-bizet.alejandro"Cassani, Davide"https://zbmath.org/authors/?q=ai:cassani.davide"Martelli, Dario"https://zbmath.org/authors/?q=ai:martelli.dario"Murthy, Sameer"https://zbmath.org/authors/?q=ai:murthy.sameerSummary: We systematically analyze the large-\(N\) limit of the superconformal index of \(\mathcal{N} = 1\) superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension. This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite. For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory. This family includes the known supersymmetric black hole solution in the holographically dual \( \mathrm{AdS}_5\) theories. We then analyze the index refined by turning on flavor chemical potentials. We show that, for a certain range of chemical potentials, the effective action again takes a universal cubic form that is controlled by the anomaly coefficients of the theory. Finally, we present a large class of solutions to the saddle-point equations which are labelled by group homomorphisms of finite abelian groups of order \(N\) into the torus.Effective theories as truncated trans-series and scale separated compactifications.https://zbmath.org/1456.813082021-04-16T16:22:00+00:00"Emelin, Maxim"https://zbmath.org/authors/?q=ai:emelin.maximSummary: We study the possibility of realizing scale-separated type IIB Anti-de Sitter and de Sitter compactifications within a controlled effective field theory regime defined by low-energy and large (but scale-separated) compactification volume. The approach we use views effective theories as truncations of the full quantum equations of motion expanded in a trans-series around this asymptotic regime. By studying the scalings of all possible perturbative and non-perturbative corrections we identify the effects that have the right scaling to allow for the desired solutions. In the case of Anti-de Sitter, we find agreement with KKLT-type scenarios, and argue that non-perturbative brane-instantons wrapping four-cycles (or similarly scaling effects) are essentially the only ingredient that allows for scale separated solutions. We also comment on the relation of these results to the AdS swampland conjectures. For the de Sitter case we find that we are forced to introduce an infinite number of relatively unsuppressed corrections to the equations of motion, leading to a breakdown of effective theory. This suggests that if de Sitter vacua exist in the string landscape, they should not be thought of as residing within the same effective theory as the AdS or Minkowski compactifications, but rather as defining a separate asymptotic regime, presumably related to the others by a duality transformation.\( \mathrm{SL}(2,\mathbb{Z})\) action on QFTs with \(\mathbb{Z}_2\) symmetry and the Brown-Kervaire invariants.https://zbmath.org/1456.814052021-04-16T16:22:00+00:00"Bhardwaj, Lakshya"https://zbmath.org/authors/?q=ai:bhardwaj.lakshya"Lee, Yasunori"https://zbmath.org/authors/?q=ai:lee.yasunori"Tachikawa, Yuji"https://zbmath.org/authors/?q=ai:tachikawa.yujiSummary: We consider an analogue of Witten's \( \mathrm{SL}(2,\mathbb{Z})\) action on three-dimensional QFTs with U(1) symmetry for \(2k\)-dimensional QFTs with \(\mathbb{Z}_2\) \( (k-1) \)-form symmetry. We show that the \( \mathrm{SL}(2,\mathbb{Z})\) action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the \( \mathrm{SL}(2,\mathbb{Z})\) anomaly of the bulk \((2k + 1)\)-dimensional \(\mathbb{Z}_2\) gauge theory.A scattering amplitude in conformal field theory.https://zbmath.org/1456.813782021-04-16T16:22:00+00:00"Gillioz, Marc"https://zbmath.org/authors/?q=ai:gillioz.marc"Meineri, Marco"https://zbmath.org/authors/?q=ai:meineri.marco"Penedones, João"https://zbmath.org/authors/?q=ai:penedones.joaoSummary: We define form factors and scattering amplitudes in conformal field theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as \(p^2 \rightarrow 0\). In particular, we study a form factor \(F(s, t, u) \) obtained from a four-point function of identical scalar primary operators. We show that \(F\) is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the \textit{3d} Ising model, perturbative fixed points and holographic CFTs.A generalized Nachtmann theorem in CFT.https://zbmath.org/1456.813892021-04-16T16:22:00+00:00"Kundu, Sandipan"https://zbmath.org/authors/?q=ai:kundu.sandipanSummary: Correlators of unitary quantum field theories in Lorentzian signature obey certain analyticity and positivity properties. For interacting unitary CFTs in more than two dimensions, we show that these properties impose general constraints on families of minimal twist operators that appear in the OPEs of primary operators. In particular, we rederive and extend the convexity theorem which states that for the family of minimal twist operators with even spins appearing in the reflection-symmetric OPE of any scalar primary, twist must be a monotonically increasing convex function of the spin. Our argument is completely non-perturbative and it also applies to the OPE of nonidentical scalar primaries in unitary CFTs, constraining the twist of spinning operators appearing in the OPE. Finally, we argue that the same methods also impose constraints on the Regge behavior of certain CFT correlators.Quantum BTZ black hole.https://zbmath.org/1456.830232021-04-16T16:22:00+00:00"Emparan, Roberto"https://zbmath.org/authors/?q=ai:emparan.roberto"Frassino, Antonia Micol"https://zbmath.org/authors/?q=ai:frassino.antonia-micol"Way, Benson"https://zbmath.org/authors/?q=ai:way.bensonSummary: We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in \( \mathrm{AdS}_4\), first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, satisfies the first law of thermodynamics exactly, even in the presence of backreaction and with higher-curvature corrections, while the Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather non-trivial bulk calculation, shows the consistency of the holographic interpretation of braneworlds. We compare our renormalized stress tensor to results derived for free conformal fields, and for a previous holographic construction without backreaction effects, which is shown to be a limit of the solutions in this article.The \(\mathcal{N}_3=3\to\mathcal{N}_3=4\) enhancement of super Chern-Simons theories in \(D=3\), Calabi HyperKähler metrics and M2-branes on the \(\mathcal{C}(\mathrm{N}^{0,1,0})\) conifold.https://zbmath.org/1456.530742021-04-16T16:22:00+00:00"Fré, P."https://zbmath.org/authors/?q=ai:fre.pietro-giuseppe"Giambrone, A."https://zbmath.org/authors/?q=ai:giambrone.adam"Grassi, P. A."https://zbmath.org/authors/?q=ai:grassi.pietro-antonio"Vasko, P."https://zbmath.org/authors/?q=ai:vasko.petrSummary: Considering matter coupled supersymmetric Chern-Simons theories in three dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement \(\mathcal{N}_3=3\to\mathcal{N}_3=4\) from the case where the hypermultiplets span a flat HyperKähler manifold to that where they live on a curved one. We derive the precise conditions of this enhancement in terms of generalized Gaiotto-Witten identities to be satisfied by the tri-holomorphic moment maps. An infinite class of HyperKähler metrics compatible with the enhancement condition is provided by the Calabi metrics on \(T^\star\mathbb{P}^n\). In this list we find, for \(n=2\) the resolution of the metric cone on \(\mathrm{N}^{0,1,0}\) which is the unique homogeneous Sasaki-Einstein 7-manifold leading to an \(\mathcal{N}_4=3\) compactification of M-theory. This leads to challenging perspectives for the discovery of new relations between the enhancement mechanism in \(D=3\), the geometry of M2-brane solutions and also for the dual description of super Chern-Simons theories on curved HyperKähler manifolds in terms of gauged fixed supergroup Chern-Simons theories.Rademacher expansions and the spectrum of 2d CFT.https://zbmath.org/1456.813472021-04-16T16:22:00+00:00"Alday, Luis F."https://zbmath.org/authors/?q=ai:alday.luis-f"Bae, Jin-Beom"https://zbmath.org/authors/?q=ai:bae.jinbeomSummary: A classical result from analytic number theory by Rademacher gives an exact formula for the Fourier coefficients of modular forms of non-positive weight. We apply similar techniques to study the spectrum of two-dimensional unitary conformal field theories, with no extended chiral algebra and \( c > 1\). By exploiting the full modular constraints of the partition function we propose an expression for the spectral density in terms of the light spectrum of the theory. The expression is given in terms of a Rademacher expansion, which converges for spin \(j \neq 0\). For a finite number of light operators the expression agrees with a variant of the Poincare construction developed by Maloney, Witten and Keller. With this framework we study the presence of negative density of states in the partition function dual to pure gravity, and propose a scenario to cure this negativity.Two interacting scalars system in curved spacetime --- vacuum stability from the curved spacetime effective field theory (cEFT) perspective.https://zbmath.org/1456.830352021-04-16T16:22:00+00:00"Lalak, Zygmunt"https://zbmath.org/authors/?q=ai:lalak.zygmunt"Nakonieczna, Anna"https://zbmath.org/authors/?q=ai:nakonieczna.anna"Nakonieczny, Łukasz"https://zbmath.org/authors/?q=ai:nakonieczny.lukaszSummary: In this article we investigated the influence of the gravity mediated higher dimensional operators on the issue of vacuum stability in a model containing two interacting scalar fields. As a framework we used the curved spacetime Effective Field Theory (cEFT) applied to the aforementioned system in which one of the scalars is heavy. After integrating out the heavy scalar we used the standard Euclidean approach to the obtained cEFT. Apart from analyzing the influence of standard operators like the non-minimal coupling to gravity and the dimension six contribution to the scalar field potential, we also investigated the rarely discussed dimension six contribution to the kinetic term and the new gravity mediated contribution to the scalar quartic self-interaction.Quasinormal modes in charged fluids at complex momentum.https://zbmath.org/1456.830432021-04-16T16:22:00+00:00"Jansen, Aron"https://zbmath.org/authors/?q=ai:jansen.aron"Pantelidou, Christiana"https://zbmath.org/authors/?q=ai:pantelidou.christianaSummary: We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordström black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.String defects, supersymmetry and the Swampland.https://zbmath.org/1456.830862021-04-16T16:22:00+00:00"Angelantonj, Carlo"https://zbmath.org/authors/?q=ai:angelantonj.carlo"Bonnefoy, Quentin"https://zbmath.org/authors/?q=ai:bonnefoy.quentin"Condeescu, Cezar"https://zbmath.org/authors/?q=ai:condeescu.cezar"Dudas, Emilian"https://zbmath.org/authors/?q=ai:dudas.emilianSummary: Recently, Kim, Shiu and Vafa proposed general consistency conditions for six dimensional supergravity theories with minimal supersymmetry coming from couplings to strings. We test them in explicit perturbative orientifold models in order to unravel the microscopic origin of these constraints. Based on the perturbative data, we conjecture the existence of null charges \(Q \bullet Q = 0\) for any six-dimensional theory with at least one tensor multiplet, coupling to string defects of charge \(Q\). We then include the new constraint to exclude some six-dimensional supersymmetric anomaly-free examples that have currently no string or F-theory realization. We also investigate the constraints from the couplings to string defects in case where supersymmetry is broken in tachyon free vacua, containing non-BPS configurations of brane supersymmetry breaking type, where the breaking is localized on antibranes. In this case, some conditions have naturally to be changed or relaxed whenever the string defects experience supersymmetry breaking, whereas the constraints are still valid if they are geometrically separated from the supersymmetry breaking source.Classical algebraic structures in string theory effective actions.https://zbmath.org/1456.830982021-04-16T16:22:00+00:00"Erbin, Harold"https://zbmath.org/authors/?q=ai:erbin.harold"Maccaferri, Carlo"https://zbmath.org/authors/?q=ai:maccaferri.carlo"Schnabl, Martin"https://zbmath.org/authors/?q=ai:schnabl.martin"Vošmera, Jakub"https://zbmath.org/authors/?q=ai:vosmera.jakubSummary: We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of \(A_\infty\) or \(L_\infty\) type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten's open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian \(A_\infty \)-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-brane deformations induced by changes in the closed string background.More on Wilson toroidal networks and torus blocks.https://zbmath.org/1456.830542021-04-16T16:22:00+00:00"Alkalaev, Konstantin"https://zbmath.org/authors/?q=ai:alkalaev.konstantin"Belavin, Vladimir"https://zbmath.org/authors/?q=ai:belavin.vladimir-aSummary: We consider the Wilson line networks of the Chern-Simons \(3d\) gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus \(2d\) CFT. After general discussion that summarizes and further extends results known in the literature we explicitly obtain the one-point torus block and two-point torus blocks through particular matrix elements of toroidal Wilson network operators in irreducible finite-dimensional representations of \(sl (2, \mathbb{R})\) algebra. The resulting expressions are given in two alternative forms using different ways to treat multiple tensor products of \(sl (2, \mathbb{R})\) representations: (1) 3\textit{mj} Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor products of the fundamental \(sl (2, \mathbb{R})\) representation.Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector.https://zbmath.org/1456.813452021-04-16T16:22:00+00:00"Wang, Rui"https://zbmath.org/authors/?q=ai:wang.rui.1|wang.rui.2|wang.rui"Wang, Shi-Kun"https://zbmath.org/authors/?q=ai:wang.shikun"Wu, Ke"https://zbmath.org/authors/?q=ai:wu.ke"Zhao, Wei-Zhong"https://zbmath.org/authors/?q=ai:zhao.weizhongSummary: We analyze the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector. We show that their partition functions can be expressed as the infinite sums of the homogeneous operators acting on the elementary functions. In spite of the fact that the usual \(W\)-representations of these matrix models can not be provided here, we can still derive the compact expressions of the correlators in these two supereigenvalue models. Furthermore, the non-Gaussian (chiral) cases are also discussed.Form factors of local operators in supersymmetric quantum integrable models.https://zbmath.org/1456.814322021-04-16T16:22:00+00:00"Fuksa, J."https://zbmath.org/authors/?q=ai:fuksa.jiri|fuksa.jan"Slavnov, N. A."https://zbmath.org/authors/?q=ai:slavnov.nikita-aBuilding bases of loop integrands.https://zbmath.org/1456.813002021-04-16T16:22:00+00:00"Bourjaily, Jacob L."https://zbmath.org/authors/?q=ai:bourjaily.jacob-l"Herrmann, Enrico"https://zbmath.org/authors/?q=ai:herrmann.enrico"Langer, Cameron"https://zbmath.org/authors/?q=ai:langer.cameron-k"Trnka, Jaroslav"https://zbmath.org/authors/?q=ai:trnka.jaroslavSummary: We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all `leading-(transcendental-)weight' contributions of \textit{any} four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent \textit{all} scattering amplitude integrands in the theory --- for generic helicities and arbitrary multiplicity.M-theoretic genesis of topological phases.https://zbmath.org/1456.813412021-04-16T16:22:00+00:00"Cho, Gil Young"https://zbmath.org/authors/?q=ai:cho.gil-young"Gang, Dongmin"https://zbmath.org/authors/?q=ai:gang.dongmin"Kim, Hee-Cheol"https://zbmath.org/authors/?q=ai:kim.hee-cheolSummary: We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction, the topological phases emerge as macroscopic world-volume theories of M5-branes wrapped around certain types of non-hyperbolic 3-manifolds. We devise a systematic algorithm for identifying the emergent topological phases from topological data of the internal wrapped 3-manifolds. As a benchmark of our approach, we reproduce all the known unitary bosonic topological orders up to rank 4. Remarkably, our construction is not restricted to an unitary bosonic theory but it can also generate fermionic and/or non-unitary anyon models in an equivalent fashion. Hence, we pave a new route toward the classification of topological phases of matter.Emergent Yang-Mills theory.https://zbmath.org/1456.830202021-04-16T16:22:00+00:00"de Mello Koch, Robert"https://zbmath.org/authors/?q=ai:de-mello-koch.robert"Huang, Jia-Hui"https://zbmath.org/authors/?q=ai:huang.jiahui"Kim, Minkyoo"https://zbmath.org/authors/?q=ai:kim.minkyoo"Van Zyl, Hendrik J. R."https://zbmath.org/authors/?q=ai:van-zyl.hendrik-j-rSummary: We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the \(\mathrm{su} (2|3)\) sector of \(\mathcal{N} = 4\) super Yang-Mills theory, have a bare dimension \(\sim N\) and are a linear combination of restricted Schur polynomials with \(p \sim O(1)\) long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problems maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of \(p\) giant graviton branes, which is a \(\mathrm{U} (p)\) Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder.Systematics of type IIA moduli stabilisation.https://zbmath.org/1456.831052021-04-16T16:22:00+00:00"Marchesano, Fernando"https://zbmath.org/authors/?q=ai:marchesano.fernando"Prieto, David"https://zbmath.org/authors/?q=ai:prieto.david"Quirant, Joan"https://zbmath.org/authors/?q=ai:quirant.joan"Shukla, Pramod"https://zbmath.org/authors/?q=ai:shukla.pramod-sSummary: We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of \(p\)-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.Random boundary geometry and gravity dual of \(T\overline{T}\) deformation.https://zbmath.org/1456.813842021-04-16T16:22:00+00:00"Hirano, Shinji"https://zbmath.org/authors/?q=ai:hirano.shinji"Shigemori, Masaki"https://zbmath.org/authors/?q=ai:shigemori.masakiSummary: We study the random geometry approach to the \(T\overline{T}\) deformation of \(2d\) conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the \(T\overline{T}\) deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of \( \mathrm{AdS}_3\) spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant \(T\overline{T}\) operator. We streamline the method of computation and calculate the energy spectrum and the thermal free energy in a manner that can be directly translated into the gravity dual language. We further generalize this approach to correlation functions and reproduce the all-order result with universal logarithmic corrections computed by Cardy in a different method. In contrast to earlier proposals, this version of the gravity dual of the \(T\overline{T}\) deformation works not only for the energy spectrum and the thermal free energy but also for correlation functions.4-point function from conformally coupled scalar in \( \mathrm{AdS}_6\).https://zbmath.org/1456.813952021-04-16T16:22:00+00:00"Oh, Jae-Hyuk"https://zbmath.org/authors/?q=ai:oh.jae-hyukSummary: We explore conformally coupled scalar theory in \( \mathrm{AdS}_6\) extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling \(\lambda \). We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension \(\Delta = 3\), from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the \(\Delta = 3\) scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect \(\operatorname{SO}(5)\) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic \(n\)-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of \(n\)-point function by connecting \(l\)-point functions each other where \( l < n \). In the co-linear limit, these \(n\)-point functions reproduce the conformal \(n\)-point functions of \(\Delta = 3\) scalar operators in \(d = 5\) Euclidean space addressed in [the author, ``A conformal scalar \(n\)-point function in momentum space'', Preprint, \url{arXiv:2001.05379}].Breaking supersymmetry with pure spinors.https://zbmath.org/1456.830492021-04-16T16:22:00+00:00"Legramandi, Andrea"https://zbmath.org/authors/?q=ai:legramandi.andrea"Tomasiello, Alessandro"https://zbmath.org/authors/?q=ai:tomasiello.alessandroSummary: For several classes of BPS vacua, we find a procedure to modify the PDEs that imply preserved supersymmetry and the equations of motion so that they still imply the latter but not the former. In each case we trace back this supersymmetry-breaking deformation to a distinct modification of the pure spinor equations that provide a geometrical interpretation of supersymmetry. We give some concrete examples: first we generalize the Imamura class of \(Mink_6\) solutions by removing a symmetry requirement, and then derive some local and global solutions both before and after breaking supersymmetry.Shocks, superconvergence, and a stringy equivalence principle.https://zbmath.org/1456.830282021-04-16T16:22:00+00:00"Koloğlu, Murat"https://zbmath.org/authors/?q=ai:kologlu.murat"Kravchuk, Petr"https://zbmath.org/authors/?q=ai:kravchuk.petr"Simmons-Duffin, David"https://zbmath.org/authors/?q=ai:simmons-duffin.david"Zhiboedov, Alexander"https://zbmath.org/authors/?q=ai:zhiboedov.alexanderSummary: We study propagation of a probe particle through a series of closely situated gravitational shocks. We argue that in any UV-complete theory of gravity the result does not depend on the shock ordering --- in other words, coincident gravitational shocks commute. Shock commutativity leads to nontrivial constraints on low-energy effective theories. In particular, it excludes non-minimal gravitational couplings unless extra degrees of freedom are judiciously added. In flat space, these constraints are encoded in the vanishing of a certain ``superconvergence sum rule.'' In AdS, shock commutativity becomes the statement that average null energy (ANEC) operators commute in the dual CFT. We prove commutativity of ANEC operators in any unitary CFT and establish sufficient conditions for commutativity of more general light-ray operators. Superconvergence sum rules on CFT data can be obtained by inserting complete sets of states between light-ray operators. In a planar 4d CFT, these sum rules express \(\frac{a-c}{c}\) in terms of the OPE data of single-trace operators.Finite-\(N\) corrections to the M-brane indices.https://zbmath.org/1456.813292021-04-16T16:22:00+00:00"Arai, Reona"https://zbmath.org/authors/?q=ai:arai.reona"Fujiwara, Shota"https://zbmath.org/authors/?q=ai:fujiwara.shota"Imamura, Yosuke"https://zbmath.org/authors/?q=ai:imamura.yosuke"Mori, Tatsuya"https://zbmath.org/authors/?q=ai:mori.tatsuya"Yokoyama, Daisuke"https://zbmath.org/authors/?q=ai:yokoyama.daisukeSummary: We investigate finite-\(N\) corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of \(N\) M2-branes we calculate the finite-\(N\) corrections as the contribution of extended M5-branes in the dual geometry \( \mathrm{AdS}_4 \times {S}^7\). We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensional theories on \(N\) M5-branes we calculate the indices by analyzing extended M2-branes in \( \mathrm{AdS}_7 \times {S}^4\). Again, we include only configurations with single wrapping. We first compare the result for \(N = 1\) with the index of the free tensor multiplet to estimate the order of the error due to multiple wrapping. We calculate first few terms of the index of \(A_N -1\) theories explicitly, and confirm that they can be expanded by superconformal representations. We also discuss multiple-wrapping contributions to the six-dimensional Schur-like index.Gauges in three-dimensional gravity and holographic fluids.https://zbmath.org/1456.830552021-04-16T16:22:00+00:00"Ciambelli, Luca"https://zbmath.org/authors/?q=ai:ciambelli.luca"Marteau, Charles"https://zbmath.org/authors/?q=ai:marteau.charles"Petropoulos, P. Marios"https://zbmath.org/authors/?q=ai:petropoulos.p-marios"Ruzziconi, Romain"https://zbmath.org/authors/?q=ai:ruzziconi.romainSummary: Solutions to Einstein's vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have been performed abundantly, several relevant questions remain. These questions include the interplay between the standard Bondi gauge and the Eddington-Finkelstein type of gauge used in the fluid/gravity holographic reconstruction of these spacetimes, as well as the Fefferman-Graham gauge, when available i.e. in anti de Sitter. The goal of the present work is to set up a thorough dictionary for the available descriptions with emphasis on the relativistic or Carrollian holographic fluids, which portray the bulk from the boundary in anti-de Sitter or flat instances. A complete presentation of residual diffeomorphisms with a preliminary study of their algebra accompanies the situations addressed here.Bethe ansatz in stringy sigma models.https://zbmath.org/1456.813372021-04-16T16:22:00+00:00"Klose, T."https://zbmath.org/authors/?q=ai:klose.thomas"Zarembo, K."https://zbmath.org/authors/?q=ai:zarembo.konstantinDoes the round sphere maximize the free energy of (2+1)-dimensional QFTs?https://zbmath.org/1456.813742021-04-16T16:22:00+00:00"Fischetti, Sebastian"https://zbmath.org/authors/?q=ai:fischetti.sebastian"Wallis, Lucas"https://zbmath.org/authors/?q=ai:wallis.lucas"Wiseman, Toby"https://zbmath.org/authors/?q=ai:wiseman.tobySummary: We examine the renormalized free energy of the free Dirac fermion and the free scalar on a (2+1)-dimensional geometry \(\mathbb{R} \times \Sigma\), with \(\Sigma\) having spherical topology and prescribed area. Using heat kernel methods, we perturbatively compute this energy when \(\Sigma\) is a small deformation of the round sphere, finding that at any temperature the round sphere is a local maximum. At low temperature the free energy difference is due to the Casimir effect. We then numerically compute this free energy for a class of large axisymmetric deformations, providing evidence that the round sphere \textit{globally} maximizes it, and we show that the free energy difference relative to the round sphere is unbounded below as the geometry on \(\Sigma\) becomes singular. Both our perturbative and numerical results in fact stem from the stronger finding that the difference between the heat kernels of the round sphere and a deformed sphere always appears to have definite sign. We investigate the relevance of our results to physical systems like monolayer graphene consisting of a membrane supporting relativistic QFT degrees of freedom.\( T\overline{T} \)-deformation of \(q\)-Yang-Mills theory.https://zbmath.org/1456.830692021-04-16T16:22:00+00:00"Santilli, Leonardo"https://zbmath.org/authors/?q=ai:santilli.leonardo"Szabo, Richard J."https://zbmath.org/authors/?q=ai:szabo.richard-j"Tierz, Miguel"https://zbmath.org/authors/?q=ai:tierz.miguelSummary: We derive the \(T\overline{T} \)-perturbed version of two-dimensional \(q\)-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the \(T\overline{T} \)-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large \(N\) factorization into chiral and anti-chiral sectors. For the \( \mathrm{U} (N)\) gauge theory on the sphere, we show that the large \(N\) phase transition persists, and that it is of third order and induced by instantons. The effect of the \(T\overline{T} \)-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for \( (q,t) \)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large \(N\) limit of Yang-Mills theory, showing that the \(T\overline{T} \)-deformation decreases the contribution of the Boltzmann entropy.Dual S-matrix bootstrap. Part I. 2D theory.https://zbmath.org/1456.814532021-04-16T16:22:00+00:00"Guerrieri, Andrea L."https://zbmath.org/authors/?q=ai:guerrieri.andrea-l"Homrich, Alexandre"https://zbmath.org/authors/?q=ai:homrich.alexandre"Vieira, Pedro"https://zbmath.org/authors/?q=ai:vieira.pedro-sampaio|vieira.pedro-gSummary: Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.Global aspects of spaces of vacua.https://zbmath.org/1456.831082021-04-16T16:22:00+00:00"Sharon, Adar"https://zbmath.org/authors/?q=ai:sharon.adarSummary: We study ``vacuum crossing'', which occurs when the vacua of a theory are exchanged as we vary some periodic parameter \(\theta\) in a closed loop. We show that vacuum crossing is a useful non-perturbative tool to study strongly-coupled quantum field theories, since finding vacuum crossing in a weakly-coupled regime of the theory can lead to nontrivial consequences in the strongly-coupled regime. We start by discussing a mechanism where vacuum crossing occurs due to an anomaly, and then discuss some applications of vacuum crossing in general. In particular, we argue that vacuum crossing can be used to check IR dualities and to look for emergent IR symmetries.On \(\alpha '\)-effects from \(D\)-branes in \(4d\) \( \mathcal{N} = 1\).https://zbmath.org/1456.813402021-04-16T16:22:00+00:00"Weissenbacher, Matthias"https://zbmath.org/authors/?q=ai:weissenbacher.matthiasSummary: In this work we study type IIB Calabi-Yau orientifold compactifications in the presence of space-time filling D7-branes and O7-planes. In particular, we conclude that \(\alpha'^2g_s\)-corrections to their DBI actions lead to a modification of the four-dimensional \(\mathcal{N} = 1\) Kähler potential and coordinates. We focus on the one-modulus case of the geometric background i.e. \(h^{1,1} = 1\) where we find that the \(\alpha'^2g_s \)-correction is of topological nature. It depends on the first Chern form of the four-cycle of the Calabi-Yau orientifold which is wrapped by the D7-branes and O7-plane. This is in agreement with our previous F-theory analysis and provides further evidence for a potential breaking of the no-scale structure at order \(\alpha'^2g_s\). Corrected background solutions for the dilaton, the warp-factor as well as the internal space metric are derived. Additionally, we briefly discuss \(\alpha '\)-corrections from other \(Dp\)-branes.The unique Polyakov blocks.https://zbmath.org/1456.814032021-04-16T16:22:00+00:00"Sleight, Charlotte"https://zbmath.org/authors/?q=ai:sleight.charlotte"Taronna, Massimo"https://zbmath.org/authors/?q=ai:taronna.massimoSummary: In this work we present a closed form expression for Polyakov blocks in Mellin space for arbitrary spin and scaling dimensions. We provide a prescription to fix the contact term ambiguity uniquely by reducing the problem to that of fixing the contact term ambiguity at the level of cyclic exchange amplitudes --- defining cyclic Polyakov blocks --- in terms of which any fully crossing symmetric correlator can be decomposed. We also give another, equivalent, prescription which does not rely on a decomposition into cyclic amplitudes. We extract the OPE data of double-twist operators in the direct channel expansion of the cyclic Polyakov blocks using and extending the analysis of [\textit{C. Sleight} and \textit{M. Taronna}, J. High Energy Phys. 2018, No. 11, Paper No. 89, 62 p. (2018; Zbl 1404.81242)] to include contributions that are non-analytic in spin. The relation between cyclic Polyakov blocks and analytic Bootstrap functionals is underlined.Large-\(N\) behavior of three-dimensional lattice \(\mathbb {CP}^{N-1}\) models.https://zbmath.org/1456.813222021-04-16T16:22:00+00:00"Pelissetto, Andrea"https://zbmath.org/authors/?q=ai:pelissetto.andrea"Vicari, Ettore"https://zbmath.org/authors/?q=ai:vicari.ettoreSingle particle operators and their correlators in free \(\mathcal{N} = 4\) SYM.https://zbmath.org/1456.814192021-04-16T16:22:00+00:00"Aprile, F."https://zbmath.org/authors/?q=ai:aprile.francesco"Drummond, J. M."https://zbmath.org/authors/?q=ai:drummond.james-m"Heslop, P."https://zbmath.org/authors/?q=ai:heslop.paul-j"Paul, H."https://zbmath.org/authors/?q=ai:paul.himadri-sekhar|paul.henning-a|paul.henrik|paul.h-g|paul.hynek|paul.harry"Sanfilippo, F."https://zbmath.org/authors/?q=ai:sanfilippo.francesco"Santagata, M."https://zbmath.org/authors/?q=ai:santagata.maria-c"Stewart, A."https://zbmath.org/authors/?q=ai:stewart.alastairSummary: We consider a set of half-BPS operators in \(\mathcal{N} = 4\) super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on \( \mathrm{AdS}_5 \times S^5\). These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. We show that single-particle \( \mathrm{U}(N)\) operators belong to the \( \mathrm{SU} (N)\) subspace, thus for length greater than one they are simply the \( \mathrm{SU} (N)\) single-particle operators. Then, we point out that at large \(N\), as the length of the operator increases, the single-particle operator naturally interpolates between the single-trace and the \(S^3\) giant graviton. At finite \(N\), the multi-particle basis, obtained by taking products of the single-particle operators, gives a new basis for all half-BPS states, and this new basis naturally cuts off when the length of any of the single-particle operators exceeds the number of colours. From the two-point function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-to-maximally extremal free correlators, and we discuss features of the correlators when the extremality is lowered. Finally, we describe a half-BPS projection of the operator product expansion on the multi-particle basis which provides an alternative construction of four- and higher-point functions in the free theory.Heterotic backgrounds via generalised geometry: moment maps and moduli.https://zbmath.org/1456.830872021-04-16T16:22:00+00:00"Ashmore, Anthony"https://zbmath.org/authors/?q=ai:ashmore.anthony"Strickland-Constable, Charles"https://zbmath.org/authors/?q=ai:strickland-constable.charles"Tennyson, David"https://zbmath.org/authors/?q=ai:tennyson.david"Waldram, Daniel"https://zbmath.org/authors/?q=ai:waldram.danielSummary: We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an \( \mathrm{SU} (3) \times \mathrm{ Spin} (6 + n)\) structure within \( \mathrm{O}(6,6+ n) \times \mathbb{R}^+\) generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kähler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator.https://zbmath.org/1456.813252021-04-16T16:22:00+00:00"Hashimoto, Koji"https://zbmath.org/authors/?q=ai:hashimoto.koji"Huh, Kyoung-Bum"https://zbmath.org/authors/?q=ai:huh.kyoung-bum"Kim, Keun-Young"https://zbmath.org/authors/?q=ai:kim.keun-young"Watanabe, Ryota"https://zbmath.org/authors/?q=ai:watanabe.ryotaSummary: We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.Ultra-stable charging of fast-scrambling SYK quantum batteries.https://zbmath.org/1456.812532021-04-16T16:22:00+00:00"Rosa, Dario"https://zbmath.org/authors/?q=ai:rosa.dario"Rossini, Davide"https://zbmath.org/authors/?q=ai:rossini.davide"Andolina, Gian Marcello"https://zbmath.org/authors/?q=ai:andolina.gian-marcello"Polini, Marco"https://zbmath.org/authors/?q=ai:polini.marco"Carrega, Matteo"https://zbmath.org/authors/?q=ai:carrega.matteoSummary: Collective behavior strongly influences the charging dynamics of quantum batteries (QBs). Here, we study the impact of nonlocal correlations on the energy stored in a system of \(N\) QBs. A unitary charging protocol based on a Sachdev-Ye-Kitaev (SYK) quench Hamiltonian is thus introduced and analyzed. SYK models describe strongly interacting systems with nonlocal correlations and fast thermalization properties. Here, we demonstrate that, once charged, the average energy stored in the QB is very stable, realizing an ultraprecise charging protocol. By studying fluctuations of the average energy stored, we show that temporal fluctuations are strongly suppressed by the presence of nonlocal correlations at all time scales. A comparison with other paradigmatic examples of many-body QBs shows that this is linked to the collective dynamics of the SYK model and its high level of entanglement. We argue that such feature relies on the fast scrambling property of the SYK Hamiltonian, and on its fast thermalization properties, promoting this as an ideal model for the ultimate temporal stability of a generic QB. Finally, we show that the temporal evolution of the ergotropy, a quantity that characterizes the amount of extractable work from a QB, can be a useful probe to infer the thermalization properties of a many-body quantum system.A-type quiver varieties and ADHM moduli spaces.https://zbmath.org/1456.140172021-04-16T16:22:00+00:00"Koroteev, Peter"https://zbmath.org/authors/?q=ai:koroteev.peterThis paper studies relation between equivariant \(K\)-theories of the framed \(A_n\)-type quiver variety \(X_n\) and of the rank \(r\) ADHM moduli space \(M_r= \bigsqcup_{k \ge 0}M_{r,k}\), where \(k\) denotes the instanton number. The \(K\)-theories considered are the equivariant quantum \(K\)-theory \(H_n:=K_{T^{n+2}}(QM(\mathbb{P}^1,X_n))\) and the equivariant \(K\)-theory \(K_{r,k}:=K_{T^2}(M_{r,k})\), where \(T\) denotes the one-dimensional torus.
The main results are Theorem 3.3 and Theorem 4.6, where an embedding \(\bigoplus_{l=0}^k K_{r,l} \hookrightarrow H_{n r}\) is constructed. The embedding is designed to map the \(T^2\)-fixed point classes in \(K_{r,l}\) to the coefficients of vertex functions in \(H_{n r}\). The construction is done by explicit calculations using Macdonald symmetric polynomials.
The paper also proposes an interesting Conjecture 5.4 which relates the eigenvalues of quantum multiplication operators in \(K\)-theory of \(M_r\) with those of the elliptic Ruijsenaars-Schneider model.
Reviewer: Shintaro Yanagida (Nagoya)Giant Wilson loops and \( \mathrm{AdS}_2/ \mathrm{dCFT}_1\).https://zbmath.org/1456.814332021-04-16T16:22:00+00:00"Giombi, Simone"https://zbmath.org/authors/?q=ai:giombi.simone"Jiang, Jiaqi"https://zbmath.org/authors/?q=ai:jiang.jiaqi"Komatsu, Shota"https://zbmath.org/authors/?q=ai:komatsu.shotaSummary: The 1/2-BPS Wilson loop in \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with \( \mathrm{AdS}_2 \times S^2\) and \( \mathrm{AdS}_2 \times S^4\) worldvolume geometries, ending at the \( \mathrm{ AdS}_5\) boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large \(N\) limit exactly as a function of the 't Hooft coupling. The results are given by simple integrals of polynomials that resemble the \(Q\)-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.Dimensional reduction and scattering formulation for even topological invariants.https://zbmath.org/1456.814942021-04-16T16:22:00+00:00"Schulz-Baldes, Hermann"https://zbmath.org/authors/?q=ai:schulz-baldes.hermann"Toniolo, Daniele"https://zbmath.org/authors/?q=ai:toniolo.danieleSummary: Strong invariants of even-dimensional topological insulators of independent Fermions are expressed in terms of an invertible operator on the Hilbert space over the boundary. It is given by the Cayley transform of the boundary restriction of the half-space resolvent. This dimensional reduction is routed in new representation for the \(K\)-theoretic exponential map. It allows to express the invariants via the reflection matrix at the Fermi energy, for the scattering set-up of a wire coupled to the half-space insulator.Area-dependent quantum field theory.https://zbmath.org/1456.814112021-04-16T16:22:00+00:00"Runkel, Ingo"https://zbmath.org/authors/?q=ai:runkel.ingo"Szegedy, Lóránt"https://zbmath.org/authors/?q=ai:szegedy.lorantSummary: Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number -- interpreted as area -- which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang-Mills theory with compact gauge group, which we treat in detail.Model-dependence of minimal-twist OPEs in \(d > 2\) holographic CFTs.https://zbmath.org/1456.830752021-04-16T16:22:00+00:00"Fitzpatrick, A. Liam"https://zbmath.org/authors/?q=ai:fitzpatrick.a-liam"Huang, Kuo-Wei"https://zbmath.org/authors/?q=ai:huang.kuo-wei"Meltzer, David"https://zbmath.org/authors/?q=ai:meltzer.david"Perlmutter, Eric"https://zbmath.org/authors/?q=ai:perlmutter.eric"Simmons-Duffin, David"https://zbmath.org/authors/?q=ai:simmons-duffin.davidSummary: Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge \(C_T\), we clarify the properties of stress tensor composite primary operators of minimal twist, \([T^m]\), using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling \(\left\langle{\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle \), where \({\mathcal{O}}_L\) is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling \(\left\langle TT{\mathcal{O}}_L\right\rangle \), the three-point coupling \(\left\langle{\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle\) is modified at large \(C_T\) if \(\left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T} \). This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to \({\mathcal{O}}_L\) can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-\( \mathcal{l} \geq 2\) bulk field at tree level, or any spin \(\mathcal{l}\) at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.Entanglement and classical fluctuations at finite-temperature critical points.https://zbmath.org/1456.810972021-04-16T16:22:00+00:00"Wald, Sascha"https://zbmath.org/authors/?q=ai:wald.sascha"Arias, Raúl"https://zbmath.org/authors/?q=ai:arias.raul-e"Alba, Vincenzo"https://zbmath.org/authors/?q=ai:alba.vincenzoPetz reconstruction in random tensor networks.https://zbmath.org/1456.813422021-04-16T16:22:00+00:00"Jia, Hewei Frederic"https://zbmath.org/authors/?q=ai:jia.hewei-frederic"Rangamani, Mukund"https://zbmath.org/authors/?q=ai:rangamani.mukundSummary: We illustrate the ideas of bulk reconstruction in the context of random tensor network toy models of holography. Specifically, we demonstrate how the Petz [\textit{D. Petz}, Commun. Math. Phys. 105, 123--131 (1986; Zbl 0597.46067)] reconstruction map works to obtain bulk operators from the boundary data by exploiting the replica trick. We also take the opportunity to comment on the differences between coarse-graining and random projections.Holography and unitarity.https://zbmath.org/1456.830782021-04-16T16:22:00+00:00"Giddings, Steven B."https://zbmath.org/authors/?q=ai:giddings.steven-bSummary: If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling \(G\). The zero coupling limit gives ordinary quantum field theory, and is therefore not necessarily expected to be holographic. This, and the structure of gravity at non-zero \(G\), raises important questions about the full map. In particular, construction of a holographic map appears to require as input a solution of the nonperturbative analog of the bulk gravitational constraints, that is, the unitary bulk evolution. Moreover, examination of the candidate boundary algebra, including the boundary hamiltonian, reveals commutators that don't close in the usual fashion expected for a boundary theory.Comments on the stability of the KPV state.https://zbmath.org/1456.830472021-04-16T16:22:00+00:00"Nguyen, Nam"https://zbmath.org/authors/?q=ai:nguyen.nam-anh|nguyen.nam-hoai|nguyen.nam-phuong|nguyen.nam-trung|nguyen.nam-ky|nguyen.nam-hai|nguyen.nam-tuanSummary: Using the blackfold approach, we study the classical stability of the KPV (Kachru-Pearson-Verlinde) state of anti-D3 branes at the tip of the Klebanov-Strassler throat. With regards to generic long-wavelength deformations considered, we found no instabilities. We comment on the relation of our results to existing results on the stability of the KPV state.Gravitational positivity bounds.https://zbmath.org/1456.830312021-04-16T16:22:00+00:00"Tokuda, Junsei"https://zbmath.org/authors/?q=ai:tokuda.junsei"Aoki, Katsuki"https://zbmath.org/authors/?q=ai:aoki.katsuki"Hirano, Shin'ichi"https://zbmath.org/authors/?q=ai:hirano.shinichiSummary: We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic \(t\)-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with ``wrong'' sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by \({M}_{ \mathrm{pl}}^{-2}\alpha^{\prime}\) where \(\alpha \)' is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed.Searching for surface defect CFTs within \( \mathrm{AdS}_3\).https://zbmath.org/1456.813732021-04-16T16:22:00+00:00"Faedo, Federico"https://zbmath.org/authors/?q=ai:faedo.federico"Lozano, Yolanda"https://zbmath.org/authors/?q=ai:lozano.yolanda"Petri, Nicolò"https://zbmath.org/authors/?q=ai:petri.nicoloSummary: We study \( \mathrm{AdS}_3 \times S^3 /{\mathbb{Z}}_k \times {\tilde{S}}^3/{\mathbb{Z}}_{k^{\prime}}\) solutions to M-theory preserving \(\mathcal{N} = (0, 4)\) supersymmetries, arising as near-horizon limits of M2-M5 brane intersections ending on M5'-branes, with both types of five-branes placed on A-type singularities. Solutions in this class asymptote locally to \( \mathrm{AdS}_7 /{\mathbb{Z}}_k\times{\tilde{S}}^3/{\mathbb{Z}}_{k^{\prime}} \), and can thus be interpreted as holographic duals to surface defect CFTs within the \(\mathcal{N} = (1, 0) 6\) d CFT dual to this solution. Upon reduction to Type IIA, we obtain a new class of solutions of the form \( \mathrm{AdS}_3 \times S^3/ \mathbb{Z}_k \times S^2 \times \Sigma_2\) preserving (0,4) supersymmetries. We construct explicit 2d quiver CFTs dual to these solutions, describing D2-D4 surface defects embedded within the 6d (1,0) quiver CFT dual to the \( \mathrm{AdS}_7/ \mathbb{Z}_k\) solution to massless IIA. Finally, in the massive case, we show that the recently constructed \( \mathrm{AdS}_3 \times S^2 \times \mathrm{CY}_2\) solutions with \(\mathcal{N} = (0, 4)\) supersymmetries gain a defect interpretation as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz \( \mathrm{AdS}_6\) background.Surface operators in superspace.https://zbmath.org/1456.814262021-04-16T16:22:00+00:00"Cremonini, C. A."https://zbmath.org/authors/?q=ai:cremonini.c-a"Grassi, P. A."https://zbmath.org/authors/?q=ai:grassi.pietro-antonio"Penati, S."https://zbmath.org/authors/?q=ai:penati.silviaSummary: We generalize the geometrical formulation of Wilson loops recently introduced in [\textit{C. A. Cremonini} et al., J. High Energy Phys. 2020, No. 4, Paper No. 161, 40 p. (2020; Zbl 1436.81133)] to the description of Wilson Surfaces. For \(N = (2, 0)\) theory in six dimensions, we provide an explicit derivation of BPS Wilson Surfaces with non-trivial coupling to scalars, together with their manifestly supersymmetric version. We derive explicit conditions which allow to classify these operators in terms of the number of preserved supercharges. We also discuss kappa-symmetry and prove that BPS conditions in six dimensions arise from kappa-symmetry invariance in eleven dimensions. Finally, we discuss super-Wilson Surfaces --- and higher dimensional operators --- as objects charged under global \(p\)-form (super)symmetries generated by tensorial supercurrents. To this end, the construction of conserved supercurrents in supermanifolds and of the corresponding conserved charges is developed in details.Momentum space spinning correlators and higher spin equations in three dimensions.https://zbmath.org/1456.813072021-04-16T16:22:00+00:00"Jain, Sachin"https://zbmath.org/authors/?q=ai:jain.sachin"John, Renjan Rajan"https://zbmath.org/authors/?q=ai:john.renjan-rajan"Malvimat, Vinay"https://zbmath.org/authors/?q=ai:malvimat.vinaySummary: In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the five-point function of the scalar operator in the free bosonic theory. We discuss techniques which are more efficient than the usual PV reduction to evaluate one loop integrals. Our techniques can be easily generalised to momentum space correlators of complicated spinning operators and to higher point functions. The three dimensional fermionic theory has the interesting feature that the scalar operator \(\overline{\psi}\psi\) is odd under parity. To account for this, we develop a parity odd basis which is useful to write correlation functions involving spinning operators and an odd number of \(\overline{\psi}\psi\) operators. We further study higher spin (HS) equations in momentum space which are algebraic in nature and hence simpler than their position space counterparts. We use them to solve for three-point functions involving spinning operators without invoking conformal invariance. However, at the level of four-point functions, solving the HS equation requires additional constraints that come from conformal invariance and we could only verify that our explicit results solve the HS equation.Twisted string theory in Anti-de Sitter space.https://zbmath.org/1456.814092021-04-16T16:22:00+00:00"Li, Songyuan"https://zbmath.org/authors/?q=ai:li.songyuan"Troost, Jan"https://zbmath.org/authors/?q=ai:troost.janSummary: We construct a string theory in three-dimensional Anti-de Sitter space-time that is independent of the boundary metric. It is a topologically twisted theory of quantum gravity. We study string theories with an asymptotic \(N = 2\) superconformal symmetry and demonstrate that, when the world sheet coupling to the space-time boundary metric undergoes a U(1) R-symmetry twist, the space-time boundary energy-momentum tensor becomes topological. As a by-product of our analysis, we obtain the world sheet vertex operator that codes the space-time energy-momentum for conformally flat boundary metrics.Landau diagrams in AdS and S-matrices from conformal correlators.https://zbmath.org/1456.814552021-04-16T16:22:00+00:00"Komatsu, Shota"https://zbmath.org/authors/?q=ai:komatsu.shota"Paulos, Miguel F."https://zbmath.org/authors/?q=ai:paulos.miguel-f"van Rees, Balt C."https://zbmath.org/authors/?q=ai:van-rees.balt-c"Zhao, Xiang"https://zbmath.org/authors/?q=ai:zhao.xiangSummary: Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in [\textit{M. F. Paulos} et al., J. High Energy Phys. 2017, No. 11, Paper No. 133, 45 p. (2017; Zbl 1383.81251)] based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called `bad regions', where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.Nonrelativistic spinning strings.https://zbmath.org/1456.831072021-04-16T16:22:00+00:00"Roychowdhury, Dibakar"https://zbmath.org/authors/?q=ai:roychowdhury.dibakarSummary: We construct nonrelativistic spinning string solutions corresponding to \( \mathrm{SU} (1, 2|3)\) Spin-Matrix theory (SMT) limit of strings in \( \mathrm{AdS}_5 \times S^5\). Considering various nonrelativistic spinning string configurations both in \( \mathrm{AdS}_5\) as well as \(S^5\) we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong coupling \(( \sim \sqrt{\mathfrak{g}})\) corrections near the BPS bound have been estimated in the slow spinning limit of strings in \( \mathrm{AdS}_5\). We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along \( \mathrm{AdS}_5\) and one along \(S^5\). Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in \( \mathrm{AdS}_5\). The rest of the paper essentially unfolds the underlying connection between \( \mathrm{SU} (1, 2|3)\) Spin-Matrix theory (SMT) limit of strings in \( \mathrm{AdS}_5 \times S^5\) and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in \( R \times S^3\) as well as in certain sub-sector of \( \mathrm{AdS}_5\) we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.Secularly growing loop corrections in scalar wave background.https://zbmath.org/1456.813142021-04-16T16:22:00+00:00"Akhmedov, E. T."https://zbmath.org/authors/?q=ai:akhmedov.emil-t"Diatlyk, O."https://zbmath.org/authors/?q=ai:diatlyk.o-nSummary: We consider two-dimensional Yukawa theory in the scalar wave background \(\varphi (t-x)\). If one takes as initial state in such a background the scalar vacuum corresponding to \(\varphi = 0\), then loop corrections to a certain part of the Keldysh propagator, corresponding to the anomalous expectation value, grow with time. That is a signal to the fact that under the kick of the \(\varphi (t-x)\) wave the scalar field rolls down the effective potential from the \(\varphi = 0\) position to the proper ground state. We show the evidence supporting these observations.Regge OPE blocks and light-ray operators.https://zbmath.org/1456.812582021-04-16T16:22:00+00:00"Kobayashi, Nozomu"https://zbmath.org/authors/?q=ai:kobayashi.nozomu"Nishioka, Tatsuma"https://zbmath.org/authors/?q=ai:nishioka.tatsuma"Okuyama, Yoshitaka"https://zbmath.org/authors/?q=ai:okuyama.yoshitakaSummary: We consider the structure of the operator product expansion (OPE) in conformal field theory by employing the OPE block formalism. The OPE block acted on the vacuum is promoted to an operator and its implications are examined on a non-vacuum state. We demonstrate that the OPE block is dominated by a light-ray operator in the Regge limit, which reproduces precisely the Regge behavior of conformal blocks when used inside scalar four-point functions. Motivated by this observation, we propose a new form of the OPE block, called the light-ray channel OPE block that has a well-behaved expansion dominated by a light-ray operator in the Regge limit. We also show that the two OPE blocks have the same asymptotic form in the Regge limit and confirm the assertion that the Regge limit of a pair of spacelike-separated operators in a Minkowski patch is equivalent to the OPE limit of a pair of timelike-separated operators associated with the original pair in a different Minkowski patch.Exact results and Schur expansions in quiver Chern-Simons-matter theories.https://zbmath.org/1456.814422021-04-16T16:22:00+00:00"Santilli, Leonardo"https://zbmath.org/authors/?q=ai:santilli.leonardo"Tierz, Miguel"https://zbmath.org/authors/?q=ai:tierz.miguelSummary: We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell's integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of \(\mathrm{U}(N\)) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters \(t_j = - e^{2 \pi m_j }\), where \(m_j\) are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.Quiver Yangian from crystal melting.https://zbmath.org/1456.812162021-04-16T16:22:00+00:00"Li, Wei"https://zbmath.org/authors/?q=ai:li.wei.7|li.wei-wayne|li.wei.10|li.wei.11|li.wei.9|li.wei.4|li.wei.8|li.wei|li.wei.3|li.wei.2"Yamazaki, Masahito"https://zbmath.org/authors/?q=ai:yamazaki.masahitoSummary: We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are ``bootstrapped'' from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact 4-cycles.``Lagrangian disks'' in M-theory.https://zbmath.org/1456.814312021-04-16T16:22:00+00:00"Franco, Sebastían"https://zbmath.org/authors/?q=ai:franco.sebastian"Gukov, Sergei"https://zbmath.org/authors/?q=ai:gukov.sergei"Lee, Sangmin"https://zbmath.org/authors/?q=ai:lee.sangmin"Seong, Rak-Kyeong"https://zbmath.org/authors/?q=ai:seong.rak-kyeong"Sparks, James"https://zbmath.org/authors/?q=ai:sparks.jamesSummary: While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in \(G_2\) holonomy spaces and to Spin(7) metrics on 8-manifolds with \(T^2\) fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories \(T[M_4]\) on the other.Comments on D3-brane holography.https://zbmath.org/1456.830732021-04-16T16:22:00+00:00"Chakraborty, Soumangsu"https://zbmath.org/authors/?q=ai:chakraborty.soumangsu"Giveon, Amit"https://zbmath.org/authors/?q=ai:giveon.amit"Kutasov, David"https://zbmath.org/authors/?q=ai:kutasov.davidSummary: We revisit the idea that the quantum dynamics of open strings ending on \(N\) D3-branes in the large \(N\) limit can be described at large `t Hooft coupling by classical closed string theory in the background created by the D3-branes in asymptotically flat spacetime. We study the resulting thermodynamics and compute the Hagedorn temperature and other properties of the D3-brane worldvolume theory in this regime. We also consider the theory in which the D3-branes are replaced by negative branes and show that its thermodynamics is well behaved. We comment on the idea that this theory can be thought of as an irrelevant deformation of \(\mathcal{N} = 4\) SYM, and on its relation to \(T\overline{T}\) deformed \( \mathrm{CFT}_2\).Dualities for three-dimensional \(\mathcal{N} = 2 \) \( \mathrm{SU} (N_c)\) chiral adjoint SQCD.https://zbmath.org/1456.814172021-04-16T16:22:00+00:00"Amariti, Antonio"https://zbmath.org/authors/?q=ai:amariti.antonio"Fazzi, Marco"https://zbmath.org/authors/?q=ai:fazzi.marcoSummary: We study dualities for 3d \(\mathcal{N} = 2 \) \( \mathrm{SU} (N_c)\) SQCD at Chern-Simons level \(k\) in presence of an adjoint with polynomial superpotential. The dualities are dubbed \textit{chiral} because there is a different amount of fundamentals \(N_f\) and antifundamentals \(N_a \). We build a complete classification of such dualities in terms of \( | N_f - N_a | \) and \(k\). The classification is obtained by studying the flow from the non-chiral case, and we corroborate our proposals by matching the three-sphere partition functions. Finally, we revisit the case of \( \mathrm{SU} (N_c)\) SQCD without the adjoint, comparing our results with previous literature.Black holes, moduli, and long-range forces.https://zbmath.org/1456.830412021-04-16T16:22:00+00:00"Heidenreich, Ben"https://zbmath.org/authors/?q=ai:heidenreich.benSummary: It is well known that an identical pair of extremal Reissner-Nordström black holes placed a large distance apart will exert no force on each other. In this paper, I establish that the same result holds in a very large class of two-derivative effective theories containing an arbitrary number of gauge fields and moduli, where the appropriate analog of an extremal Reissner-Nordström black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanishing horizon area. Analogous results hold for black branes.Edge modes of gravity. II: Corner metric and Lorentz charges.https://zbmath.org/1456.830242021-04-16T16:22:00+00:00"Freidel, Laurent"https://zbmath.org/authors/?q=ai:freidel.laurent"Geiller, Marc"https://zbmath.org/authors/?q=ai:geiller.marc"Pranzetti, Daniele"https://zbmath.org/authors/?q=ai:pranzetti.danieleSummary: In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local \(\mathfrak{sl} (2, \mathbb{C})\) component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local \(\mathfrak{sl} (2, \mathbb{R})\) algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.
For Part I, see [the authors, J. High Energy Phys. 2020, No. 11, Paper No. 26, 51 p. (2020; Zbl 07326009)].A note on membrane interactions and the scalar potential.https://zbmath.org/1456.813352021-04-16T16:22:00+00:00"Herraez, Alvaro"https://zbmath.org/authors/?q=ai:herraez.alvaroSummary: We compute the tree-level potential between two parallel \(p\)-branes due to the exchange of scalars, gravitons and \((p+1)\)-forms. In the case of BPS membranes in 4d \(\mathcal{N} = 1\) supergravity, this provides an interesting reinterpretation of the classical Cremmer et al. formula for the F-term scalar potential in terms of scalar, graviton and 3-form exchange. In this way, we present a correspondence between the scalar potential at every point in scalar field space and a system of two interacting BPS membranes. This could potentially lead to interesting implications for the Swampland Program by providing a concrete way to relate conjectures about the form of scalar potentials with conjectures regarding the spectrum of charged objects.Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and \(3D\) bosonization.https://zbmath.org/1456.830832021-04-16T16:22:00+00:00"Li, Zhijin"https://zbmath.org/authors/?q=ai:li.zhijinSummary: Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary 't Hooft coupling \(\lambda\) in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the \(\lambda\) expansions of the correlation functions. The \(\lambda\) expansions terminate at order \(\lambda^2\) and the solutions are exact in \(\lambda\). Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the \(3D\) Chern-Simons vector models and their holographic duals in \(\mathrm{AdS}_4\). Besides, we show that the same results can also be obtained rather simply from bosonization duality of \(3D\) Chern-Simons vector models. The odd term at order \(O( \lambda)\) in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the \(3D\) bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents.S matrix for a three-parameter integrable deformation of \( \mathrm{AdS}_3 \times S^3\) strings.https://zbmath.org/1456.814512021-04-16T16:22:00+00:00"Bocconcello, Marco"https://zbmath.org/authors/?q=ai:bocconcello.marco"Masuda, Isari"https://zbmath.org/authors/?q=ai:masuda.isari"Seibold, Fiona K."https://zbmath.org/authors/?q=ai:seibold.fiona-k"Sfondrini, Alessandro"https://zbmath.org/authors/?q=ai:sfondrini.alessandroSummary: We consider the three-parameter integrable deformation of the \( \mathrm{AdS}_3 \times S^3\) superstring background constructed in [\textit{F. Delduc} et al., J. High Energy Phys. 2019, No. 1, Paper No. 109, 25 p. (2019; Zbl 1414.81129)]. Working on the string worldsheet in uniform lightcone gauge, we find the tree-level bosonic S matrix of the model and study some of its limits.Sigma models with local couplings: a new integrability-RG flow connection.https://zbmath.org/1456.831022021-04-16T16:22:00+00:00"Hoare, Ben"https://zbmath.org/authors/?q=ai:hoare.ben"Levine, Nat"https://zbmath.org/authors/?q=ai:levine.nat"Tseytlin, Arkady A."https://zbmath.org/authors/?q=ai:tseytlin.arkady-aSummary: We consider several classes of \(\sigma \)-models (on groups and symmetric spaces, \( \eta \)-models, \( \lambda \)-models) with local couplings that may depend on the 2d coordinates, e.g. on time \(\tau \). We observe that (i) starting with a classically integrable 2d \(\sigma \)-model, (ii) formally promoting its couplings \(h_\alpha\) to functions \(h_\alpha(\tau) \) of 2d time, and (iii) demanding that the resulting time-dependent model also admits a Lax connection implies that \(h_\alpha(\tau)\) must solve the 1-loop RG equations of the original theory with \(\tau\) interpreted as RG time. This provides a novel example of an `integrability-RG flow' connection. The existence of a Lax connection suggests that these time-dependent \(\sigma \)-models may themselves be understood as integrable. We investigate this question by studying the possibility of constructing non-local and local conserved charges. Such \(\sigma \)-models with \(D\)-dimensional target space and time-dependent couplings subject to the RG flow naturally appear in string theory upon fixing the light-cone gauge in a \((D + 2)\)-dimensional conformal \(\sigma \)-model with a metric admitting a covariantly constant null Killing vector and a dilaton linear in the null coordinate.Curvature constraints in heterotic Landau-Ginzburg models.https://zbmath.org/1456.830992021-04-16T16:22:00+00:00"Garavuso, Richard S."https://zbmath.org/authors/?q=ai:garavuso.richard-sSummary: In this paper, we study a class of heterotic Landau-Ginzburg models. We show that the action can be written as a sum of BRST-exact and non-exact terms. The non-exact terms involve the pullback of the complexified Kähler form to the worldsheet and terms arising from the superpotential, which is a Grassmann-odd holomorphic function of the superfields. We then demonstrate that the action is invariant on-shell under supersymmetry transformations up to a total derivative. Finally, we extend the analysis to the case in which the superpotential is not holomorphic. In this case, we find that supersymmetry imposes a constraint which relates the nonholomorphic parameters of the superpotential to the Hermitian curvature. Various special cases of this constraint have previously been used to establish properties of Mathai-Quillen form analogues which arise in the corresponding heterotic Landau-Ginzburg models. There, it was claimed that supersymmetry imposes those constraints. Our goal in this paper is to support that claim. The analysis for the nonholomorphic case also reveals a constraint imposed by supersymmetry that we did not anticipate from studies of Mathai-Quillen form analogues.The Regge limit of \( \mathrm{AdS}_3\) holographic correlators.https://zbmath.org/1456.830792021-04-16T16:22:00+00:00"Giusto, Stefano"https://zbmath.org/authors/?q=ai:giusto.stefano"Hughes, Marcel R. R."https://zbmath.org/authors/?q=ai:hughes.marcel-r-r"Russo, Rodolfo"https://zbmath.org/authors/?q=ai:russo.rodolfoSummary: We study the Regge limit of 4-point \( \mathrm{AdS}_3 \times S^3\) correlators in the tree-level supergravity approximation and provide various explicit checks of the relation between the eikonal phase derived in the bulk picture and the anomalous dimensions of certain double-trace operators. We consider both correlators involving all light operators and HHLL correlators with two light and two heavy multi-particle states. These heavy operators have a conformal dimension proportional to the central charge and are pure states of the theory, dual to asymptotically \( \mathrm{AdS}_3 \times S^3\) regular geometries. Deviation from \( \mathrm{AdS}_3 \times S^3\) is parametrised by a scale \(\mu\) and is related to the conformal dimension of the dual heavy operator. In the HHLL case, we work at leading order in \(\mu\) and derive the CFT data relevant to the bootstrap relations in the Regge limit. Specifically, we show that the minimal solution to these equations relevant for the conical defect geometries is different to the solution implied by the microstate geometries dual to pure states.Modular invariance in superstring theory from \(\mathcal{N} = 4\) super-Yang-Mills.https://zbmath.org/1456.814242021-04-16T16:22:00+00:00"Chester, Shai M."https://zbmath.org/authors/?q=ai:chester.shai-m"Green, Michael B."https://zbmath.org/authors/?q=ai:green.michael-b"Pufu, Silviu S."https://zbmath.org/authors/?q=ai:pufu.silviu-s"Wang, Yifan"https://zbmath.org/authors/?q=ai:wang.yifan"Wen, Congkao"https://zbmath.org/authors/?q=ai:wen.congkaoSummary: We study the four-point function of the lowest-lying half-BPS operators in the \(\mathcal{N} = 4\) \( \mathrm{SU} (N)\) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-\(N\) expansion in which the complexified Yang-Mills coupling \(\tau\) is fixed. In this expansion, non-perturbative instanton contributions are present, and the \( \mathrm{SL} (2, \mathbb{Z})\) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed \(\mathcal{N} = 4\) SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to \(N^2- 1\) and are independent of \(\tau\) and \(\overline{\tau} \), we find that the terms of order \(\sqrt{N}\) and \(1/\sqrt{N}\) in the large \(N\) expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series \(E\left(\frac{3}{2},\tau, \overline{\tau}\right)\) and \(E\left(\frac{5}{2},\tau, \overline{\tau}\right) \), respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from \(R^4\) and \(D^4R^4\) contact interactions, which, for the \(R^4\) case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order \({N}^{\frac{1}{2}-m}\) with integer \(m \geq 0 \), the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly \( \mathrm{SL} (2, \mathbb{Z})\) invariant.Supersymmetric quantum spherical spins with short-range interactions.https://zbmath.org/1456.812072021-04-16T16:22:00+00:00"Tavares, L. V. T."https://zbmath.org/authors/?q=ai:tavares.l-v-t"dos Santos, L. G."https://zbmath.org/authors/?q=ai:dos-santos.l-g"Landi, G. T."https://zbmath.org/authors/?q=ai:landi.gabriel-t"Gomes, Pedro R. S."https://zbmath.org/authors/?q=ai:gomes.pedro-r-s"Bienzobaz, P. F."https://zbmath.org/authors/?q=ai:bienzobaz.p-fDeformed Cauchy random matrix ensembles and large \(N\) phase transitions.https://zbmath.org/1456.813442021-04-16T16:22:00+00:00"Russo, Jorge G."https://zbmath.org/authors/?q=ai:russo.jorge-gSummary: We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large \(N\) third-order phase transition.Probing the Planck scale: the modification of the time evolution operator due to the quantum structure of spacetime.https://zbmath.org/1456.830292021-04-16T16:22:00+00:00"Padmanabhan, T."https://zbmath.org/authors/?q=ai:padmanabhan.t-v|padmanabhan.thanuSummary: The propagator which evolves the wave-function in non-relativistic quantum mechanics, can be expressed as a matrix element of a time evolution operator: i.e. \(G_{ \mathrm{NR}}(x) = \langle \mathbf{x}_2|U_{ \mathrm{NR}}(t)|\mathbf{x}_1 \rangle \) in terms of the orthonormal eigenkets \( | \mathbf{x} \rangle \) of the position operator. In quantum field theory, it is not possible to define a conceptually useful single-particle position operator or its eigenkets. It is also not possible to interpret the relativistic (Feynman) propagator \(G_R(x)\) as evolving any kind of single-particle wave-functions. In spite of all these, it is indeed possible to express the propagator of a free spinless particle, in quantum field theory, as a matrix element \( \langle \mathbf{x}_2|U_R(t)|\mathbf{x}_1 \rangle \) for a suitably defined time evolution operator and (non-orthonormal) kets \( | \mathbf{x} \rangle \) labeled by spatial coordinates. At mesoscopic scales, which are close but not too close to Planck scale, one can incorporate quantum gravitational corrections to the propagator by introducing a zero-point-length. It turns out that even this quantum-gravity-corrected propagator can be expressed as a matrix element \( \langle \mathbf{x}_2 | U_{ \mathrm{QG}}(t)|\mathbf{x}_1 \rangle \). I describe these results and explore several consequences. It turns out that the evolution operator \(U_{ \mathrm{QG}}(t)\) becomes non-unitary for sub-Planckian time intervals while remaining unitary for time interval is larger than Planck time. The results can be generalized to any ultrastatic curved spacetime.Virasoro blocks and quasimodular forms.https://zbmath.org/1456.813672021-04-16T16:22:00+00:00"Das, Diptarka"https://zbmath.org/authors/?q=ai:das.diptarka"Datta, Shouvik"https://zbmath.org/authors/?q=ai:datta.shouvik"Raman, Madhusudhan"https://zbmath.org/authors/?q=ai:raman.madhusudhanSummary: We analyse Virasoro blocks in the regime of heavy intermediate exchange (\(h_p \rightarrow \infty\)). For the 1-point block on the torus and the 4-point block on the sphere, we show that each order in the large-\(h_p\) expansion can be written in closed form as polynomials in the Eisenstein series. The appearance of this structure is explained using the fusion kernel and, more markedly, by invoking the modular anomaly equations via the 2d/4d correspondence. The existence of these constraints allows us to develop a faster algorithm to recursively construct the blocks in this regime. We then apply our results to find corrections to averaged heavy-heavy-light OPE coefficients.Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT.https://zbmath.org/1456.813832021-04-16T16:22:00+00:00"Hijano, Eliot"https://zbmath.org/authors/?q=ai:hijano.eliot"Neuenfeld, Dominik"https://zbmath.org/authors/?q=ai:neuenfeld.dominikSummary: S-matrix elements in flat space can be obtained from a large AdS-radius limit of certain CFT correlators. We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space. This is done by taking the flat limit of bulk operator reconstruction techniques. Using this method, we obtain explicit expressions for incoming and outgoing U(1) gauge fields. Weinberg soft photon theorems then follow from Ward identites of conserved CFT currents. In four bulk dimensions, gauge fields on AdS can be quantized with standard and alternative boundary conditions. Changing the quantization scheme corresponds to the \(S\)-transformation of \(\mathrm{SL}(2, \mathbb{Z})\) electric-magnetic duality in the bulk. This allows us to derive both, the electric and magnetic soft photon theorems in flat space from CFT physics.Duality and supersymmetry constraints on the weak gravity conjecture.https://zbmath.org/1456.830112021-04-16T16:22:00+00:00"Loges, Gregory J."https://zbmath.org/authors/?q=ai:loges.gregory-j"Noumi, Toshifumi"https://zbmath.org/authors/?q=ai:noumi.toshifumi"Shiu, Gary"https://zbmath.org/authors/?q=ai:shiu.garySummary: Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved \( \mathrm{SL}(2, \mathbb{R})\) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved \( \mathrm{O}( d, d; \mathbb{R})\) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.Enhanced corrections near holographic entanglement transitions: a chaotic case study.https://zbmath.org/1456.830742021-04-16T16:22:00+00:00"Dong, Xi"https://zbmath.org/authors/?q=ai:dong.xi"Wang, Huajia"https://zbmath.org/authors/?q=ai:wang.huajiaSummary: Recent work found an enhanced correction to the entanglement entropy of a subsystem in a chaotic energy eigenstate. The enhanced correction appears near a phase transition in the entanglement entropy that happens when the subsystem size is half of the entire system size. Here we study the appearance of such enhanced corrections holo-graphically. We show explicitly how to find these corrections in the example of chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry. With the help of an emergent rotational symmetry, the sum over all saddle points is written in terms of an effective action for cosmic branes. The resulting Renyi and entanglement entropies are then naturally organized in a basis of fixed-area states and can be evaluated directly, showing an enhanced correction near holographic entanglement transitions. We comment on several intriguing features of our tractable example and discuss the implications for finding a convincing derivation of the enhanced corrections in other, more general holographic examples.Temperature as a quantum observable.https://zbmath.org/1456.810662021-04-16T16:22:00+00:00"Ghonge, Sushrut"https://zbmath.org/authors/?q=ai:ghonge.sushrut"Vural, Dervis Can"https://zbmath.org/authors/?q=ai:vural.dervis-canComplexity measures from geometric actions on Virasoro and Kac-Moody orbits.https://zbmath.org/1456.813712021-04-16T16:22:00+00:00"Erdmenger, Johanna"https://zbmath.org/authors/?q=ai:erdmenger.johanna"Gerbershagen, Marius"https://zbmath.org/authors/?q=ai:gerbershagen.marius"Weigel, Anna-Lena"https://zbmath.org/authors/?q=ai:weigel.anna-lenaSummary: We further advance the study of the notion of computational complexity for 2d CFTs based on a gate set built out of conformal symmetry transformations. Previously, it was shown that by choosing a suitable cost function, the resulting complexity functional is equivalent to geometric (group) actions on coadjoint orbits of the Virasoro group, up to a term that originates from the central extension. We show that this term can be recovered by modifying the cost function, making the equivalence exact. Moreover, we generalize our approach to Kac-Moody symmetry groups, finding again an exact equivalence between complexity functionals and geometric actions. We then determine the optimal circuits for these complexity measures and calculate the corresponding costs for several examples of optimal transformations. In the Virasoro case, we find that for all choices of reference state except for the vacuum state, the complexity only measures the cost associated to phase changes, while assigning zero cost to the non-phase changing part of the transformation. For Kac-Moody groups in contrast, there do exist non-trivial optimal transformations beyond phase changes that contribute to the complexity, yielding a finite gauge invariant result. Moreover, we also show that our Virasoro complexity proposal is equivalent to the on-shell value of the Liouville action, which is a complexity functional proposed in the context of path integral optimization. This equivalence provides an interpretation for the path integral optimization proposal in terms of a gate set and reference state. Finally, we further develop a new proposal for a complexity definition for the Virasoro group that measures the cost associated to non-trivial transformations beyond phase changes. This proposal is based on a cost function given by a metric on the Lie group of conformal transformations. The minimization of the corresponding complexity functional is achieved using the Euler-Arnold method yielding the Korteweg-de Vries equation as equation of motion.Towards an explicit construction of de Sitter solutions in classical supergravity.https://zbmath.org/1456.830092021-04-16T16:22:00+00:00"Kim, Nakwoo"https://zbmath.org/authors/?q=ai:kim.nakwooSummary: We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds \(O8_\pm\), proposed by \textit{C. Córdova} et al. [``Classical de Sitter solutions of 10-dimensional supergravity'', Phys. rev. Lett. 122, No. 9, Article ID 091601, 5 p. (2019; \url{doi:10.1103/PhysRevLett.122.091601})]. While the original analysis of the supergravity equations is largely numerical, we obtain semi-analytic solutions by treating the curvature as a perturbative parameter. At each order we verify that the (permissive) boundary conditions at the orientifolds are satisfied. To illustrate the advantage of our result, we calculate the four-dimensional Newton constant as a function of the cosmological constant. We also discuss how the discontinuities at \(O8_-\) can be accounted for in terms of corrections to the worldvolume action.Geometry of bounded critical phenomena.https://zbmath.org/1456.813802021-04-16T16:22:00+00:00"Gori, Giacomo"https://zbmath.org/authors/?q=ai:gori.giacomo"Trombettoni, Andrea"https://zbmath.org/authors/?q=ai:trombettoni.andreaEntanglement negativity and conformal field theory: a Monte Carlo study.https://zbmath.org/1456.829692021-04-16T16:22:00+00:00"Alba, Vincenzo"https://zbmath.org/authors/?q=ai:alba.vincenzoThe UV fate of anomalous U(1)s and the Swampland.https://zbmath.org/1456.830952021-04-16T16:22:00+00:00"Craig, Nathaniel"https://zbmath.org/authors/?q=ai:craig.nathaniel"Garcia, Isabel Garcia"https://zbmath.org/authors/?q=ai:garcia-garcia.isabel"Kribs, Graham D."https://zbmath.org/authors/?q=ai:kribs.graham-dSummary: Massive U(1) gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity. We study four-dimensional, chiral U(1) gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions. We show that such theories must be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled --- a Stückelberg limit does not exist. When the infrared fermion spectrum contains a mixed U(1)-gravitational anomaly, this class of theories provides a toy model of a boundary into the Swampland, for sufficiently small values of the vector mass. In this context, we show that the limit of a parametrically light vector comes at the cost of a quantum gravity scale that lies parametrically below \(M_{ \mathrm{Pl}}\), and our result provides field theoretic evidence for the existence of a Swampland of EFTs that is disconnected from the subset of theories compatible with a gravitational UV-completion. Moreover, when the low energy theory also contains a \( \mathrm{U}(1)^3\) anomaly, the Weak Gravity Conjecture scale makes an appearance in the form of a quantum gravity cutoff for values of the gauge coupling above a certain critical size.No-go theorem for boson condensation in topologically ordered quantum liquids.https://zbmath.org/1456.814102021-04-16T16:22:00+00:00"Neupert, Titus"https://zbmath.org/authors/?q=ai:neupert.titus"He, Huan"https://zbmath.org/authors/?q=ai:he.huan"von Keyserlingk, Curt"https://zbmath.org/authors/?q=ai:von-keyserlingk.curt"Sierra, Germán"https://zbmath.org/authors/?q=ai:sierra.german"Bernevig, B. Andrei"https://zbmath.org/authors/?q=ai:bernevig.bogdan-andreiQuantum thermalization and Virasoro symmetry.https://zbmath.org/1456.813522021-04-16T16:22:00+00:00"Beşken, Mert"https://zbmath.org/authors/?q=ai:besken.mert"Datta, Shouvik"https://zbmath.org/authors/?q=ai:datta.shouvik"Kraus, Per"https://zbmath.org/authors/?q=ai:kraus.perExact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry.https://zbmath.org/1456.814142021-04-16T16:22:00+00:00"Dantchev, Daniel M."https://zbmath.org/authors/?q=ai:danchev.daniel-mOn three-point functions in ABJM and the latitude Wilson loop.https://zbmath.org/1456.813532021-04-16T16:22:00+00:00"Bianchi, Marco S."https://zbmath.org/authors/?q=ai:bianchi.marco-sSummary: I consider three-point functions of twist-one operators in ABJM at weak coupling. I compute the structure constant of correlators involving one twist-one un-protected operator and two protected ones for a few finite values of the spin, up to two-loop order. As an application I enforce a limit on the gauge group ranks, in which I relate the structure constant for three chiral primary operators to the expectation value of a supersymmetric Wilson loop. Such a relation is then used to perform a successful five-loop test on the matrix model conjectured to describe the supersymmetric Wilson loop.Conformal field theory and the non-abelian \(\text{SU} (2)_k\) chiral spin liquid.https://zbmath.org/1456.813982021-04-16T16:22:00+00:00"Quella, Thomas"https://zbmath.org/authors/?q=ai:quella.thomas"Roy, Abhishek"https://zbmath.org/authors/?q=ai:roy.abhishekABJM theory as a Fermi gas.https://zbmath.org/1456.814402021-04-16T16:22:00+00:00"Mariño, Marcos"https://zbmath.org/authors/?q=ai:marino.marcos"Putrov, Pavel"https://zbmath.org/authors/?q=ai:putrov.pavelThe Hamilton-Jacobi equation and holographic renormalization group flows on sphere.https://zbmath.org/1456.830822021-04-16T16:22:00+00:00"Kim, Nakwoo"https://zbmath.org/authors/?q=ai:kim.nakwoo"Kim, Se-Jin"https://zbmath.org/authors/?q=ai:kim.se-jinSummary: We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton's characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.The ubiquitous ``c '': from the Stefan-Boltzmann law to quantum information*.https://zbmath.org/1456.813632021-04-16T16:22:00+00:00"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-lSignature of quantum chaos in operator entanglement in 2D CFTs.https://zbmath.org/1456.813922021-04-16T16:22:00+00:00"Nie, Laimei"https://zbmath.org/authors/?q=ai:nie.laimei"Nozaki, Masahiro"https://zbmath.org/authors/?q=ai:nozaki.masahiro"Ryu, Shinsei"https://zbmath.org/authors/?q=ai:ryu.shinsei"Tan, Mao Tian"https://zbmath.org/authors/?q=ai:tan.mao-tianConifold dynamics and axion monodromies.https://zbmath.org/1456.813392021-04-16T16:22:00+00:00"Scalisi, M."https://zbmath.org/authors/?q=ai:scalisi.marco"Soler, P."https://zbmath.org/authors/?q=ai:soler.pablo"Van Hemelryck, V."https://zbmath.org/authors/?q=ai:van-hemelryck.v"Van Riet, T."https://zbmath.org/authors/?q=ai:van-riet.thomasSummary: It has recently been appreciated that the conifold modulus plays an important role in string-phenomenological set-ups involving warped throats, both by imposing constraints on model building and for obtaining a 10-dimensional picture of SUSY-breaking. In this note, we point out that the stability of the conifold modulus furthermore prevents large super-Planckian axion monodromy field ranges caused by brane-flux decay processes down warped throats. Our findings imply a significant challenge for concrete string theory embeddings of the inflationary flux-unwinding scenario.Entanglement entropy of two disjoint intervals from fusion algebra of twist fields.https://zbmath.org/1456.813992021-04-16T16:22:00+00:00"Rajabpour, M. A."https://zbmath.org/authors/?q=ai:rajabpour.mohammad-ali"Gliozzi, F."https://zbmath.org/authors/?q=ai:gliozzi.ferdinandoTwo-cylinder entanglement entropy under a twist.https://zbmath.org/1456.813652021-04-16T16:22:00+00:00"Chen, Xiao"https://zbmath.org/authors/?q=ai:chen.xiao.1"Witczak-Krempa, William"https://zbmath.org/authors/?q=ai:witczak-krempa.william"Faulkner, Thomas"https://zbmath.org/authors/?q=ai:faulkner.thomas"Fradkin, Eduardo"https://zbmath.org/authors/?q=ai:fradkin.eduardoAnother derivation of the geometrical KPZ relations.https://zbmath.org/1456.813232021-04-16T16:22:00+00:00"David, François"https://zbmath.org/authors/?q=ai:david.francois"Bauer, Michel"https://zbmath.org/authors/?q=ai:bauer.michelWind on the boundary for the abelian sandpile model.https://zbmath.org/1456.821772021-04-16T16:22:00+00:00"Ruelle, Philippe"https://zbmath.org/authors/?q=ai:ruelle.philippeOn TCS \(G_2\) manifolds and 4D emergent strings.https://zbmath.org/1456.831092021-04-16T16:22:00+00:00"Xu, Fengjun"https://zbmath.org/authors/?q=ai:xu.fengjunSummary: In this note, we study the Swampland Distance Conjecture in TCS \(G_2\) manifold compactifications of M-theory. In particular, we are interested in testing a refined version --- the Emergent String Conjecture, in settings with 4d \(N = 1\) supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the \(K3\)-fiber in a TCS \(G_2\) manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking \(K3\)-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS \(G_2\) compactifications, which might lead to a weakly coupled fundamental type II string theory.Universal distribution of random matrix eigenvalues near the ``birth of a cut'' transition.https://zbmath.org/1456.813722021-04-16T16:22:00+00:00"Eynard, B."https://zbmath.org/authors/?q=ai:eynard.bertrandConfluence of geodesic paths and separating loops in large planar quadrangulations.https://zbmath.org/1456.822312021-04-16T16:22:00+00:00"Bouttier, J."https://zbmath.org/authors/?q=ai:bouttier.jeremie"Guitter, E."https://zbmath.org/authors/?q=ai:guitter.emmanuelProperties of field functionals and characterization of local functionals.https://zbmath.org/1456.812962021-04-16T16:22:00+00:00"Brouder, Christian"https://zbmath.org/authors/?q=ai:brouder.christian"Dang, Nguyen Viet"https://zbmath.org/authors/?q=ai:dang.nguyen-viet"Laurent-Gengoux, Camille"https://zbmath.org/authors/?q=ai:laurent-gengoux.camille"Rejzner, Kasia"https://zbmath.org/authors/?q=ai:rejzner.kasiaSummary: Functionals (i.e., functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincaré lemma and defining multi-vector fields and graded functionals within our framework.{
\copyright 2018 American Institute of Physics}Distributions of extremal black holes in Calabi-Yau compactifications.https://zbmath.org/1456.830422021-04-16T16:22:00+00:00"Hulsey, George"https://zbmath.org/authors/?q=ai:hulsey.george"Kachru, Shamit"https://zbmath.org/authors/?q=ai:kachru.shamit"Yang, Sungyeon"https://zbmath.org/authors/?q=ai:yang.sungyeon"Zimet, Max"https://zbmath.org/authors/?q=ai:zimet.maxSummary: We study non-supersymmetric extremal black hole excitations of 4d \(\mathcal{N} = 2\) supersymmetric string vacua arising from compactification on Calabi-Yau threefolds. The values of the (vector multiplet) moduli at the black hole horizon are governed by the attractor mechanism. This raises natural questions, such as ``what is the distribution of attractor points on moduli space?'' and ``how many attractor black holes are there with horizon area up to a certain size?'' We employ tools developed by \textit{F. Denef} and \textit{M. R. Douglas} [``Distributions of flux vacua'', J. High Energy Phys. 2004, No. 5, Paper No. 072, 46 p. (2004; \url{doi:10.1088/1126-6708/2004/05/072})] to answer these questions.Rényi entanglement entropies in quantum dimer models: from criticality to topological order.https://zbmath.org/1456.821912021-04-16T16:22:00+00:00"Stéphan, Jean-Marie"https://zbmath.org/authors/?q=ai:stephan.jean-marie"Misguich, Grégoire"https://zbmath.org/authors/?q=ai:misguich.gregoire"Pasquier, Vincent"https://zbmath.org/authors/?q=ai:pasquier.vincentFusion algebra of critical percolation.https://zbmath.org/1456.812182021-04-16T16:22:00+00:00"Rasmussen, Jørgen"https://zbmath.org/authors/?q=ai:rasmussen.jorgen|rasmussen.jorgen-born|rasmussen.jorgen-h"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-aA construction of infinitely many solutions to the Strominger system.https://zbmath.org/1456.813342021-04-16T16:22:00+00:00"Fei, Teng"https://zbmath.org/authors/?q=ai:fei.teng.1|fei.teng"Huang, Zhijie"https://zbmath.org/authors/?q=ai:huang.zhijie"Picard, Sebastien"https://zbmath.org/authors/?q=ai:picard.sebastienFrom the introduction:: As for compact Kähler Calabi-Yau manifolds (treated as solutions to
the Strominger system), it is widely speculated that in each dimension
there are only finitely many deformation types and hence finitely many
sets of Hodge numbers. Moreover, there are no explicit expressions for
Calabi-Yau metrics except for the flat case.\par\vspace{1mm}
In this paper, we demonstrate that the non-Kähler world of solu-
tions to the Strominger system is considerably different. More pre-
cisely, we construct explicit smooth solutions to the Strominger system
on compact non-Kähler Calabi-Yau 3-folds with infinitely many topo-
logical types and sets of Hodge numbersA cubic deformation of ABJM: the squashed, stretched, warped, and perturbed gets invaded.https://zbmath.org/1456.831132021-04-16T16:22:00+00:00"Cesàro, Mattia"https://zbmath.org/authors/?q=ai:cesaro.mattia"Larios, Gabriel"https://zbmath.org/authors/?q=ai:larios.gabriel"Varela, Oscar"https://zbmath.org/authors/?q=ai:varela.oscarSummary: A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new \(\mathcal{N} = 2\) superconformal phase. This is holographically dual to a warped \(\mathrm{ AdS}_4 \times_w S^7\) solution of M-theory equipped with a squashed and stretched metric on \(S^7\). We determine the spectrum of spin-2 operators of the cubic deformation at low energies by computing the spectrum of Kaluza-Klein (KK) gravitons over the dual \(\mathrm{AdS}_4\) solution. We calculate, numerically, the complete graviton spectrum and, analytically, the spectrum of gravitons that belong to short multiplets. We also use group theory to assess the structure of the full KK spectrum, and conclude that \(\mathcal{N} = 2\) supermultiplets cannot be allocated KK level by KK level. This phenomenon, usually referred to as ``space invaders scenario'', is also known to occur for another \(\mathrm{AdS}_4\) solution based on a different squashed \(S^7\).Momentum space CFT correlators for Hamiltonian truncation.https://zbmath.org/1456.813492021-04-16T16:22:00+00:00"Anand, Nikhil"https://zbmath.org/authors/?q=ai:anand.nikhil"Khandker, Zuhair U."https://zbmath.org/authors/?q=ai:khandker.zuhair-u"Walters, Matthew T."https://zbmath.org/authors/?q=ai:walters.matthew-tSummary: We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding to a Hamiltonian density) carries zero spatial momentum, but otherwise allowing operators to have arbitrary spin. A direct application of our formulas is the computation of Hamiltonian matrix elements within the framework of conformal truncation, a recently proposed method for numerically studying strongly-coupled QFTs in real time and infinite volume. Our momentum space formulas take the form of finite sums over \(_2F_1\) hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d \(\varphi^4\)-theory, thus providing the seed ingredients for future truncation studies.The KW equations and the Nahm pole boundary condition with knots.https://zbmath.org/1456.813112021-04-16T16:22:00+00:00"Mazzeo, Rafe"https://zbmath.org/authors/?q=ai:mazzeo.rafe-r"Witten, Edward"https://zbmath.org/authors/?q=ai:witten.edwardIn this detailed technical paper the authors extend further their previous analysis of the Kapustin-Witten (KW) equations with Nahm pole boundary condition now adapted to general 4-manifolds-with-boundary such that the boundary-3-manifold contains a knot or more generally a link.
The motivation is a conjecture of the second author that the coefficients of the Laurent expansion of the Jones polynomial of a link \(L\subset {\mathbb R}^3\) arise by counting solutions of the KW equations on the half-space \({\mathbb R}^4_+\) obeying a generalized Nahm pole boundary condition on \(\partial {\mathbb R}^4_+={\mathbb R}^3\supset L\) i.e. the Nahm pole boundary condition generalized to be compatible with the extra information of containing a link on the boundary. Roughly this means to prescribe further singularities in the Higgs field part of the KW pair along each link component while the connection part is continuous up to the boundary as before. The conjecture is important because it is well-known that computing the Jones polynomial of a link is an exponentially difficult problem in terms of e.g. the crossing number of any plane diagram of the link.
Reviewer: Gabor Etesi (Budapest)An operational construction of the sum of two non-commuting observables in quantum theory and related constructions.https://zbmath.org/1456.810102021-04-16T16:22:00+00:00"Drago, Nicolò"https://zbmath.org/authors/?q=ai:drago.nicolo"Mazzucchi, Sonia"https://zbmath.org/authors/?q=ai:mazzucchi.sonia"Moretti, Valter"https://zbmath.org/authors/?q=ai:moretti.valterSummary: The existence of a real linear space structure on the set of observables of a quantum system -- i.e., the requirement that the linear combination of two generally non-commuting observables \(A, B\) is an observable as well -- is a fundamental postulate of the quantum theory yet before introducing any structure of algebra. However, it is by no means clear how to choose the measuring instrument of a general observable of the form \(aA+bB\) (\(a,b\in\mathbb{R}\)) if such measuring instruments are given for the addends observables \(A\) and \(B\) when they are incompatible observables. A mathematical version of this dilemma is how to construct the spectral measure of \(f(aA+bB)\) out of the spectral measures of \(A\) and \(B\). We present such a construction with a formula which is valid for general unbounded self-adjoint operators \(A\) and \(B\), whose spectral measures may not commute, and a wide class of functions \(f: \mathbb{R}\rightarrow\mathbb{C} \). In the bounded case, we prove that the Jordan product of \(A\) and \(B\) (and suitably symmetrized polynomials of \(A\) and \(B)\) can be constructed with the same procedure out of the spectral measures of \(A\) and \(B\). The formula turns out to have an interesting operational interpretation and, in particular cases, a nice interplay with the theory of Feynman path integration and the Feynman-Kac formula.Aharonov-Bohm superselection sectors.https://zbmath.org/1456.812972021-04-16T16:22:00+00:00"Dappiaggi, Claudio"https://zbmath.org/authors/?q=ai:dappiaggi.claudio"Ruzzi, Giuseppe"https://zbmath.org/authors/?q=ai:ruzzi.giuseppe"Vasselli, Ezio"https://zbmath.org/authors/?q=ai:vasselli.ezioSummary: We show that the Aharonov-Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this ``topological'' quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov-Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov-Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-abelian generalizations of this effect are possible only on spacetimes with a non-abelian fundamental group.On the integrable structure of the Ising model.https://zbmath.org/1456.812492021-04-16T16:22:00+00:00"Nigro, Alessandro"https://zbmath.org/authors/?q=ai:nigro.alessandroEntanglement negativity in extended systems: a field theoretical approach.https://zbmath.org/1456.813622021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-l"Tonni, Erik"https://zbmath.org/authors/?q=ai:tonni.erikEntanglement entropy of two disjoint intervals in \(c = 1\) theories.https://zbmath.org/1456.813462021-04-16T16:22:00+00:00"Alba, Vincenzo"https://zbmath.org/authors/?q=ai:alba.vincenzo"Tagliacozzo, Luca"https://zbmath.org/authors/?q=ai:tagliacozzo.luca"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasqualeBoundary loop models and 2D quantum gravity.https://zbmath.org/1456.813882021-04-16T16:22:00+00:00"Kostov, Ivan"https://zbmath.org/authors/?q=ai:kostov.ivan-kWilson loop algebras and quantum K-theory for Grassmannians.https://zbmath.org/1456.814352021-04-16T16:22:00+00:00"Jockers, Hans"https://zbmath.org/authors/?q=ai:jockers.hans"Mayr, Peter"https://zbmath.org/authors/?q=ai:mayr.peter"Ninad, Urmi"https://zbmath.org/authors/?q=ai:ninad.urmi"Tabler, Alexander"https://zbmath.org/authors/?q=ai:tabler.alexanderSummary: We study the algebra of Wilson line operators in three-dimensional \(\mathcal{N} = 2\) supersymmetric \(\mathrm{U}(M)\) gauge theories with a Higgs phase related to a complex Grassmannian \(\mathrm{Gr}(M,N)\), and its connection to K-theoretic Gromov-Witten invariants for \(\mathrm{Gr}(M,N)\). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of \(\mathrm{Gr}(M,N)\), isomorphic to the Verlinde algebra for \(\mathrm{U}(M)\), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.Schramm-Loewner evolution in the three-state Potts model -- a numerical study.https://zbmath.org/1456.829722021-04-16T16:22:00+00:00"Gamsa, Adam"https://zbmath.org/authors/?q=ai:gamsa.adam"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-lThe Jordan structure of two-dimensional loop models.https://zbmath.org/1456.823002021-04-16T16:22:00+00:00"Morin-Duchesne, Alexi"https://zbmath.org/authors/?q=ai:morin-duchesne.alexi"Saint-Aubin, Yvan"https://zbmath.org/authors/?q=ai:saint-aubin.yvanHypotrochoids in conformal restriction systems and Virasoro descendants.https://zbmath.org/1456.813692021-04-16T16:22:00+00:00"Doyon, Benjamin"https://zbmath.org/authors/?q=ai:doyon.benjaminThe Virasoro fusion kernel and Ruijsenaars' hypergeometric function.https://zbmath.org/1456.814002021-04-16T16:22:00+00:00"Roussillon, Julien"https://zbmath.org/authors/?q=ai:roussillon.julienSummary: We show that the Virasoro fusion kernel is equal to Ruijsenaars' hypergeometric function up to normalization. More precisely, we prove that the Virasoro fusion kernel is a joint eigenfunction of four difference operators. We find a renormalized version of this kernel for which the four difference operators are mapped to four versions of the quantum relativistic hyperbolic Calogero-Moser Hamiltonian tied with the root system \(BC_1\). We consequently prove that the renormalized Virasoro fusion kernel and the corresponding quantum eigenfunction, the (renormalized) Ruijsenaars hypergeometric function, are equal.Spectral expansion for finite temperature two-point functions and clustering.https://zbmath.org/1456.813282021-04-16T16:22:00+00:00"Szécsényi, I. M."https://zbmath.org/authors/?q=ai:szecsenyi.istvan-m"Takács, G."https://zbmath.org/authors/?q=ai:takacs.gabriel|takacs.gergely|takacs.gaborThe SU(3) spin model with chemical potential by series expansion techniques.https://zbmath.org/1456.813212021-04-16T16:22:00+00:00"Kim, Jangho"https://zbmath.org/authors/?q=ai:kim.jangho"Pham, Anh Quang"https://zbmath.org/authors/?q=ai:pham.anh-quang"Philipsen, Owe"https://zbmath.org/authors/?q=ai:philipsen.owe"Scheunert, Jonas"https://zbmath.org/authors/?q=ai:scheunert.jonasSummary: The SU(3) spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be fully determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end points agree with numerical determinations to \(\mathcal{O} (1\%)\) and \(\mathcal{O} (10\%)\), respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.Lifting heptagon symbols to functions.https://zbmath.org/1456.814282021-04-16T16:22:00+00:00"Dixon, Lance J."https://zbmath.org/authors/?q=ai:dixon.lance-j"Liu, Yu-Ting"https://zbmath.org/authors/?q=ai:liu.yutingSummary: Seven-point amplitudes in planar \(\mathcal{N} = 4\) super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual functions, by specifying their first derivatives and boundary conditions on a particular two-dimensional surface. To do this, we impose branch-cut conditions and construct the entire heptagon function space through weight six. We plot the amplitudes on a few lines in the bulk Euclidean region, and explore the properties of the heptagon function space under the coaction associated with multiple polylogarithms.The Riemann zeros and the cyclic renormalization group.https://zbmath.org/1456.813182021-04-16T16:22:00+00:00"Sierra, Germán"https://zbmath.org/authors/?q=ai:sierra.germanThermodynamics of quantum spin chains with competing interactions.https://zbmath.org/1456.820772021-04-16T16:22:00+00:00"Tavares, T. S."https://zbmath.org/authors/?q=ai:tavares.t-sean"Ribeiro, G. A. P."https://zbmath.org/authors/?q=ai:ribeiro.g-a-pFeynman integrals and periods in configuration spaces.https://zbmath.org/1456.811922021-04-16T16:22:00+00:00"Ceyhan, Özgür"https://zbmath.org/authors/?q=ai:ceyhan.ozgur"Marcolli, Matilde"https://zbmath.org/authors/?q=ai:marcolli.matildeThe authors study Feynman amplitudes on two different configuration spaces. The first considered configuration space is the classical configuration space appearing in qunatum field theory. Whereas, the second considered configuration space can be understood as complexification of the first one.
The overall question through out the article is whether a Feynman amplitude is in the class of mixed Tate periods/motives or non-mixed Tate. To do so, the authors have used on the different configuration spaces different techniques.
For the classical configuration space, explicit calculations are performed with analytic methods commonly used in physics for configuration space computations. The Greens function is expanded in so-called Gegenbauer polynomials to separated the spherical part of the integration from the radial part. After some technical lemmata, an exact result is provided for the leading order term of the spherical integration of banana graph with three edges in four spacetime dimensions. The result consists of a restricted nested sum similar to the nested sums of multiple polylogarithms.
It is further proved that this restricted nested sum is expressible in terms of Mordell-Tornheim and Apostol-Vu multiple series. These series are in turn expressible by multiple zeta values and therefore mixed Tate periods. Consequently, the selected example and similar expressions for other Feynman amplitude are mixed Tate periods.
The Feynman amplitudes in the complexified configuration space are studied with algebro-geometric techniques. The configuration space is compactified with the so-called wonderful compactification, which is a generalization of the Fulton-MacPherson compactification. The pullback of the differential forms and of the chain of integration to the compactified space is developed. It is argued that the Feynman amplitudes are expressible as an integral of an algebraic differential form over a variety with mixed Tate motive, where the algebraic differential forms are not necessarily defined over the rationals.
Since the amplitudes need in general regularization to avoid divergencies, this is additionally done for the complex configuration space in two different ways after compactification. The first way is the current-regularization via residue current and principle value current. The second regularization method is a regularization via deformation, where the complex compactified configuration space is extended by a trivial fibration. The property of being a mixed Tate motive is for both regularizations preserved.
In summary, the article underpins the observation that a big class of Feynman amplitudes consists of mixed Tate periods/motives. Very interesting examples are considered, computed and constructed, which gives rise to further investigations for more general results. The relevance is of a good type for the mathematical physics community.
For the entire collection see [Zbl 1446.81001].
Reviewer: Alexander Hock (Münster)T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in \(\alpha '\).https://zbmath.org/1456.830972021-04-16T16:22:00+00:00"Elgood, Zachary"https://zbmath.org/authors/?q=ai:elgood.zachary"Ortín, Tomás"https://zbmath.org/authors/?q=ai:ortin.tomasSummary: We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter \(\alpha '\) and re-derive the \(\alpha '\)-corrected Buscher rules first found in [\textit{E. Bergshoeff} et al., Classical Quantum Gravity 13, No. 3, 321--343 (1996; Zbl 0849.53074)], proving the T duality invariance of the dimensionally-reduced action to that order in \(\alpha '\). We use Iyer and Wald's prescription to derive an entropy formula that can be applied to black hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the \(\alpha '\)-corrected T duality transformations. This formula has been successfully applied to \(\alpha '\)-corrected 4-dimensional non-extremal Reissner-Nordström black holes in [\textit{P. A. Cano} et al., J. High Energy Phys. 2020, No. 2, Paper No. 31, 31 p. (2020; Zbl 1435.83077)] and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.Carroll versus Galilei from a brane perspective.https://zbmath.org/1456.830012021-04-16T16:22:00+00:00"Bergshoeff, Eric"https://zbmath.org/authors/?q=ai:bergshoeff.eric-a"Izquierdo, José Manuel"https://zbmath.org/authors/?q=ai:izquierdo.jose-manuel"Romano, Luca"https://zbmath.org/authors/?q=ai:romano.lucaSummary: We show that our previous work [\textit{E. Bergshoeff} et al., J. High Energy Phys. 2017, No. 3, Paper No. 165, 26 p. (2017; Zbl 1377.83073)] on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to \(p\)-branes \((p = 0, 1, 2, \dots)\). Within this wider brane perspective, we make use of a formal map, given in the literature, between the corresponding \(p\)-brane Carroll and Galilei algebras where the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. This leads among other things in 3D to a map between Galilei particles and Carroll strings and in 4D to a similar map between Galilei strings and Carroll strings. We show that this formal map extends to the corresponding Lie algebra expansion of the Poincaré algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. We use this formal map to construct several new examples of Carroll gravity actions. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the \(p\)-brane sigma model action and apply this formal symmetry to give several examples of \(3D\) and \(4D\) particles and strings in a curved Carroll background.Two-dimensional \(O(n)\) models and logarithmic CFTs.https://zbmath.org/1456.813162021-04-16T16:22:00+00:00"Gorbenko, Victor"https://zbmath.org/authors/?q=ai:gorbenko.victor"Zan, Bernardo"https://zbmath.org/authors/?q=ai:zan.bernardoSummary: We study \(O(n)\)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of \(n\) below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG flow. When \(n\) is equal to two, which corresponds to the Kosterlitz-Thouless critical theory, the fixed points collide. We find that for \(n\) generic these CFTs are logarithmic and contain negative norm states; in particular, the \(O(n)\) currents belong to a staggered logarithmic multiplet. Using a conformal bootstrap approach we trace how the negative norm states decouple at \(n = 2\), restoring unitarity. The IR fixed point possesses a local relevant operator, singlet under all known global symmetries of the CFT, and, nevertheless, it can be reached by an RG flow without tuning. Besides, we observe logarithmic correlators in the closely related Potts model.Thermodynamics of accuracy in kinetic proofreading: dissipation and efficiency trade-offs.https://zbmath.org/1456.813272021-04-16T16:22:00+00:00"Rao, Riccardo"https://zbmath.org/authors/?q=ai:rao.riccardo"Peliti, Luca"https://zbmath.org/authors/?q=ai:peliti.lucaThe topological symmetric orbifold.https://zbmath.org/1456.814082021-04-16T16:22:00+00:00"Li, Songyuan"https://zbmath.org/authors/?q=ai:li.songyuan"Troost, Jan"https://zbmath.org/authors/?q=ai:troost.janSummary: We analyze topological orbifold conformal field theories on the symmetric product of a complex surface \(M\). By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by Hurwitz numbers. This proves a conjecture in the physics literature on extremal correlators. Moreover, it allows to leverage results on the combinatorics of the symmetric group to compute more structure constants explicitly. We recall that the full orbifold chiral ring is given by a symmetric orbifold Frobenius algebra. This construction enables the computation of topological genus zero and genus one correlators, and to prove the vanishing of higher genus contributions. The efficient description of all topological correlators sets the stage for a proof of a topological AdS/CFT correspondence. Indeed, we propose a concrete mathematical incarnation of the proof, relating Gromow-Witten theory in the bulk to the cohomology of the Hilbert scheme on the boundary.Holomorphic parafermions in the Potts model and stochastic Loewner evolution.https://zbmath.org/1456.821762021-04-16T16:22:00+00:00"Riva, V."https://zbmath.org/authors/?q=ai:riva.valentina"Cardy, J."https://zbmath.org/authors/?q=ai:cardy.john-lStrings and super-Yang-Mills theory: the integrable story.https://zbmath.org/1456.814432021-04-16T16:22:00+00:00"Schäfer-Nameki, Sakura"https://zbmath.org/authors/?q=ai:schafer-nameki.sakura(no abstract)The \(\mathrm{SU}(N)\) self-dual sine-Gordon model and competing orders.https://zbmath.org/1456.812982021-04-16T16:22:00+00:00"Lecheminant, P."https://zbmath.org/authors/?q=ai:lecheminant.philippe"Totsuka, K."https://zbmath.org/authors/?q=ai:totsuka.keisukeHorizon radiation reaction forces.https://zbmath.org/1456.830332021-04-16T16:22:00+00:00"Goldberger, Walter D."https://zbmath.org/authors/?q=ai:goldberger.walter-d"Rothstein, Ira Z."https://zbmath.org/authors/?q=ai:rothstein.ira-zSummary: Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton's constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).Single-interface Casimir torque.https://zbmath.org/1456.740272021-04-16T16:22:00+00:00"Morgado, Tiago A."https://zbmath.org/authors/?q=ai:morgado.tiago-a"Silveirinha, Mário G."https://zbmath.org/authors/?q=ai:silveirinha.mario-gIntegrability and transcendentality.https://zbmath.org/1456.814302021-04-16T16:22:00+00:00"Eden, Burkhard"https://zbmath.org/authors/?q=ai:eden.burkhard"Staudacher, Matthias"https://zbmath.org/authors/?q=ai:staudacher.matthiasA singular radial connection over \(\mathbb B^5\) minimizing the Yang-Mills energy.https://zbmath.org/1456.580152021-04-16T16:22:00+00:00"Petrache, Mircea"https://zbmath.org/authors/?q=ai:petrache.mirceaSummary: We prove that the pullback of the \(\mathrm{SU}(n)\)-soliton of Chern number \(c_2=1\) over \(\mathbb S^4\) via the radial projection \(\pi :\mathbb B^5{\setminus }\{0\}\to \mathbb S^4\) minimizes the Yang-Mills energy under a topologically fixed boundary trace constraint. In particular this shows that stationary Yang-Mills connections in high dimension can have singular sets of codimension 5.CFT description of the fully frustrated \(XY\) model and phase diagram analysis.https://zbmath.org/1456.813662021-04-16T16:22:00+00:00"Cristofano, Gerardo"https://zbmath.org/authors/?q=ai:cristofano.gerardo"Marotta, Vincenzo"https://zbmath.org/authors/?q=ai:marotta.vincenzo-e"Minnhagen, Petter"https://zbmath.org/authors/?q=ai:minnhagen.petter"Naddeo, Adele"https://zbmath.org/authors/?q=ai:naddeo.adele"Niccoli, Giuliano"https://zbmath.org/authors/?q=ai:niccoli.giulianoThe entanglement entropy of solvable lattice models.https://zbmath.org/1456.823242021-04-16T16:22:00+00:00"Weston, Robert"https://zbmath.org/authors/?q=ai:weston.robert-aInfrared properties of boundaries in one-dimensional quantum systems.https://zbmath.org/1456.824002021-04-16T16:22:00+00:00"Friedan, Daniel"https://zbmath.org/authors/?q=ai:friedan.daniel-harry"Konechny, Anatoly"https://zbmath.org/authors/?q=ai:konechny.anatolyBMS modular diaries: torus one-point function.https://zbmath.org/1456.813502021-04-16T16:22:00+00:00"Bagchi, Arjun"https://zbmath.org/authors/?q=ai:bagchi.arjun"Nandi, Poulami"https://zbmath.org/authors/?q=ai:nandi.poulami"Saha, Amartya"https://zbmath.org/authors/?q=ai:saha.amartya"Zodinmawia"https://zbmath.org/authors/?q=ai:zodinmawia.Summary: Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results.Random transverse field Ising model on the Cayley tree: analysis via boundary strong disorder renormalization.https://zbmath.org/1456.825202021-04-16T16:22:00+00:00"Monthus, Cécile"https://zbmath.org/authors/?q=ai:monthus.cecile"Garel, Thomas"https://zbmath.org/authors/?q=ai:garel.thomasRelaxing unimodularity for Yang-Baxter deformed strings.https://zbmath.org/1456.831032021-04-16T16:22:00+00:00"Hronek, Stanislav"https://zbmath.org/authors/?q=ai:hronek.stanislav"Wulff, Linus"https://zbmath.org/authors/?q=ai:wulff.linusSummary: We consider so-called Yang-Baxter deformations of bosonic string sigma- models, based on an \(R\)-matrix solving the (modified) classical Yang-Baxter equation. It is known that a unimodularity condition on \(R\) is sufficient for Weyl invariance at least to two loops (first order in \(\alpha^\prime)\). Here we ask what the necessary condition is. We find that in cases where the matrix \((G + B)_{ mn }\), constructed from the metric and \(B\)-field of the undeformed background, is degenerate the unimodularity condition arising at one loop can be replaced by weaker conditions. We further show that for non-unimodular deformations satisfying the one-loop conditions the Weyl invariance extends at least to two loops (first order in \(\alpha^\prime)\). The calculations are simplified by working in an \(O(D,D)\)-covariant doubled formulation.The density of critical percolation clusters touching the boundaries of strips and squares.https://zbmath.org/1456.824772021-04-16T16:22:00+00:00"Simmons, Jacob J. H."https://zbmath.org/authors/?q=ai:simmons.jacob-j-h"Kleban, Peter"https://zbmath.org/authors/?q=ai:kleban.peter"Dahlberg, Kevin"https://zbmath.org/authors/?q=ai:dahlberg.kevin"Ziff, Robert M."https://zbmath.org/authors/?q=ai:ziff.robert-mGeometric integration on Lie groups using the Cayley transform with focus on lattice QCD.https://zbmath.org/1456.814562021-04-16T16:22:00+00:00"Wandelt, Michèle"https://zbmath.org/authors/?q=ai:wandelt.michele"Günther, Michael"https://zbmath.org/authors/?q=ai:gunther.michael"Muniz, Michelle"https://zbmath.org/authors/?q=ai:muniz.michelleSummary: This work deals with geometric numerical integration on a Lie group using the Cayley transformation. We investigate a coupled system of differential equations in a Lie group setting that occurs in Lattice Quantum Chromodynamics. To simulate elementary particles, expectation values of some operators are computed using the Hybrid Monte Carlo method. In this context, Hamiltonian equations of motion in a non-abelian setting are solved with a time-reversible and volume-preserving integration method. Usually, the exponential function is used in the integration method to map the Lie algebra to the Lie group. In this paper, the focus is on geometric numerical integration using the Cayley transformation instead of the exponential function. The geometric properties of the method are shown for the example of the Störmer-Verlet method. Moreover, the advantages and disadvantages of both mappings are discussed.Analytic properties of the free energy: the tricritical Ising model.https://zbmath.org/1456.823972021-04-16T16:22:00+00:00"Mossa, Alessandro"https://zbmath.org/authors/?q=ai:mossa.alessandro"Mussardo, Giuseppe"https://zbmath.org/authors/?q=ai:mussardo.giuseppeModuli stabilisation and the statistics of SUSY breaking in the landscape.https://zbmath.org/1456.831112021-04-16T16:22:00+00:00"Broeckel, Igor"https://zbmath.org/authors/?q=ai:broeckel.igor"Cicoli, Michele"https://zbmath.org/authors/?q=ai:cicoli.michele"Maharana, Anshuman"https://zbmath.org/authors/?q=ai:maharana.anshuman"Singh, Kajal"https://zbmath.org/authors/?q=ai:singh.kajal"Sinha, Kuver"https://zbmath.org/authors/?q=ai:sinha.kuverSummary: The statistics of the supersymmetry breaking scale in the string landscape has been extensively studied in the past finding either a power-law behaviour induced by uniform distributions of F-terms or a logarithmic distribution motivated by dynamical supersymmetry breaking. These studies focused mainly on type IIB flux compactifications but did not systematically incorporate the Kähler moduli. In this paper we point out that the inclusion of the Kähler moduli is crucial to understand the distribution of the supersymmetry breaking scale in the landscape since in general one obtains unstable vacua when the F-terms of the dilaton and the complex structure moduli are larger than the F- terms of the Kähler moduli. After taking Kähler moduli stabilisation into account, we find that the distribution of the gravitino mass and the soft terms is power-law only in KKLT and perturbatively stabilised vacua which therefore favour high scale supersymmetry. On the other hand, LVS vacua feature a logarithmic distribution of soft terms and thus a preference for lower scales of supersymmetry breaking. Whether the landscape of type IIB flux vacua predicts a logarithmic or power-law distribution of the supersymmetry breaking scale thus depends on the relative preponderance of LVS and KKLT vacua.Quantum quenches in extended systems.https://zbmath.org/1456.813582021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-lEntanglement Hamiltonians in two-dimensional conformal field theory.https://zbmath.org/1456.813642021-04-16T16:22:00+00:00"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-l"Tonni, Erik"https://zbmath.org/authors/?q=ai:tonni.erikThe \((2 + 1)-d U(1)\) quantum link model masquerading as deconfined criticality.https://zbmath.org/1456.813092021-04-16T16:22:00+00:00"Banerjee, D."https://zbmath.org/authors/?q=ai:banerjee.dipayan|banerjee.dyuti-s|banerjee.deb|banerjee.debargha|banerjee.dilip-k|banerjee.debapratim|banerjee.dipak-k|banerjee.debika|banerjee.debamalya|banerjee.durga|banerjee.dibyendu|banerjee.debasish|banerjee.dipti|banerjee.debdyuti|banerjee.dhruba|banerjee.debjyoti|banerjee.dean"Jiang, F.-J."https://zbmath.org/authors/?q=ai:jiang.fengjian|jiang.fangjiao|jiang.feng-jiao"Widmer, P."https://zbmath.org/authors/?q=ai:widmer.p"Wiese, U.-J."https://zbmath.org/authors/?q=ai:wiese.uwe-jensRecent results on \(4d\) \(\mathcal{N}=2\) SCFT and singularity theory.https://zbmath.org/1456.814232021-04-16T16:22:00+00:00"Chen, Bingyi"https://zbmath.org/authors/?q=ai:chen.bingyi"Xie, Dan"https://zbmath.org/authors/?q=ai:xie.dan"Yau, Stephen S.-T."https://zbmath.org/authors/?q=ai:yau.stephen-shing-toung"Yau, Shing-Tung"https://zbmath.org/authors/?q=ai:yau.shing-tung"Zuo, Huaiqing"https://zbmath.org/authors/?q=ai:zuo.huaiqingSummary: The purpose of this paper is to summarize the results that we have obtained recently on four dimensional \(\mathcal{N}=2\) superconformal field theories from the point of view of singularity theory.
For the entire collection see [Zbl 1454.00056].Holographic Floquet states in low dimensions.https://zbmath.org/1456.830772021-04-16T16:22:00+00:00"Garbayo, Ana"https://zbmath.org/authors/?q=ai:garbayo.ana"Mas, Javier"https://zbmath.org/authors/?q=ai:mas.javier"Ramallo, Alfonso V."https://zbmath.org/authors/?q=ai:ramallo.alfonso-vSummary: We study the response of a (2+1)-dimensional gauge theory to an external rotating electric field. In the strong coupling regime such system is formulated holographically in a top-down model constructed by intersecting D3- and D5-branes along 2+1 dimensions, in the quenched approximation, in which the D5-brane is a probe in the \(\mathrm{AdS}_5 \times {\mathbb{S}}^5\) geometry. The system has a non-equilibrium phase diagram with conductive and insulator phases. The external driving induces a rotating current due to vacuum polarization (in the insulator phase) and to Schwinger effect (in the conductive phase). For some particular values of the driving frequency the external field resonates with the vector mesons of the model and a rotating current can be produced even in the limit of vanishing driving field. These features are in common with the (3+1) dimensional setup based on the D3-D7 brane model and hint on some interesting universality. We also compute the conductivities paying special attention to the photovoltaic induced Hall effect, which is only present for massive charged carriers. In the vicinity of the Floquet condensate the optical Hall coefficient persists at zero driving field, signalling time reversal symmetry breaking.Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories.https://zbmath.org/1456.814152021-04-16T16:22:00+00:00"Rajabpour, M. A."https://zbmath.org/authors/?q=ai:rajabpour.mohammad-aliOn the Vilkovisky-DeWitt approach and renormalization group in effective quantum gravity.https://zbmath.org/1456.830252021-04-16T16:22:00+00:00"Giacchini, Breno L."https://zbmath.org/authors/?q=ai:giacchini.breno-loureiro"de Paula Netto, Tibério"https://zbmath.org/authors/?q=ai:de-paula-netto.tiberio"Shapiro, Ilya L."https://zbmath.org/authors/?q=ai:shapiro.ilya-lSummary: The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the renormalization-group framework in a consistent way. On the other hand, the version of effective action proposed by Vilkovisky and DeWitt does not depend on the gauge-fixing and parametrization off- shell, opening the way to explore the running of the cosmological and Newton constants as well as the coefficients of the higher-derivative terms of the total action. We argue that in the effective framework the one-loop beta functions for the zero-, two- and four-derivative terms can be regarded as exact, that means, free from corrections coming from the higher loops. In this perspective, the running describes the renormalization group flow between the present-day Hubble scale in the IR and the Planck scale in the UV.Making the case for causal dynamical triangulations.https://zbmath.org/1456.830182021-04-16T16:22:00+00:00"Cooperman, Joshua H."https://zbmath.org/authors/?q=ai:cooperman.joshua-hSummary: The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet comprehensive, impartial yet personal presentation of the causal dynamical triangulations approach.The non-SUSY \(\mathrm{AdS}_6\) and \(\mathrm{AdS}_7\) fixed points are brane-jet unstable.https://zbmath.org/1456.831182021-04-16T16:22:00+00:00"Suh, Minwoo"https://zbmath.org/authors/?q=ai:suh.minwooSummary: In six- and seven-dimensional gauged supergravity, each scalar potential has one supersymmetric and one non-supersymmetric fixed points. The non-supersymmetric \(\mathrm{AdS}_7\) fixed point is perturbatively unstable. On the other hand, the non-supersymmetric \(\mathrm{AdS}_6\) fixed point is known to be perturbatively stable. In this note we examine the newly proposed non-perturbative decay channel, called brane-jet instabilities of the \(\mathrm{ AdS}_6\) and \(\mathrm{AdS}_7\) vacua. We find that when they are uplifted to massive type IIA and eleven-dimensional supergravity, respectively, the non-supersymmetric \(\mathrm{AdS}_6\) and \(\mathrm{AdS}_7\) vacua are both brane-jet unstable, in fond of the weak gravity conjecture.Spin clusters and conformal field theory.https://zbmath.org/1456.829712021-04-16T16:22:00+00:00"Delfino, G."https://zbmath.org/authors/?q=ai:delfino.gesualdo"Picco, M."https://zbmath.org/authors/?q=ai:picco.marco"Santachiara, R."https://zbmath.org/authors/?q=ai:santachiara.raoul"Viti, J."https://zbmath.org/authors/?q=ai:viti.jacopoMonodromy charge in D7-brane inflation.https://zbmath.org/1456.813362021-04-16T16:22:00+00:00"Kim, Manki"https://zbmath.org/authors/?q=ai:kim.manki"McAllister, Liam"https://zbmath.org/authors/?q=ai:mcallister.liamSummary: In axion monodromy inflation, traversing \(N\) axion periods corresponds to discharging \(N\) units of a quantized charge. In certain models with moving D7-branes, such as Higgs-otic inflation, this monodromy charge is D3-brane charge induced on the D7-branes. The stress-energy of the induced charge affects the internal space, changing the inflaton potential and potentially limiting the field range. We compute the backreaction of induced D3-brane charge in Higgs-otic inflation. The effect on the nonperturbative superpotential is dramatic even for \(N = 1\), and may preclude large-field inflation in this model in the absence of a mechanism to control the backreaction.Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor.https://zbmath.org/1456.813172021-04-16T16:22:00+00:00"Pulmann, Ján"https://zbmath.org/authors/?q=ai:pulmann.jan"Ševera, Pavol"https://zbmath.org/authors/?q=ai:severa.pavol"Youmans, Donald R."https://zbmath.org/authors/?q=ai:youmans.donald-rSummary: We find a Chern-Simons propagator on the ball with the chiral boundary condition. We use it to study perturbatively Chern-Simons boundary conditions related to 2-dim \(\sigma\)-models and to Poisson-Lie T-duality. In particular, we find their renormalization group flow, given by the generalized Ricci tensor. Finally we briefly discuss what happens when the Chern-Simons theory is replaced by a Courant \(\sigma\)-model or possibly by a more general AKSZ model.On matrix models and their \(q\)-deformations.https://zbmath.org/1456.814222021-04-16T16:22:00+00:00"Cassia, Luca"https://zbmath.org/authors/?q=ai:cassia.luca"Lodin, Rebecca"https://zbmath.org/authors/?q=ai:lodin.rebecca"Zabzine, Maxim"https://zbmath.org/authors/?q=ai:zabzine.maximSummary: Motivated by the BPS/CFT correspondence, we explore the similarities between the classical \(\beta\)-deformed Hermitean matrix model and the \(q\)-deformed matrix models associated to 3d \(\mathcal{N} = 2\) supersymmetric gauge theories on \(D^2 \times_q S^1\) and \({S}_b^3\) by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the \(W\)-algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.Exact solution of an \(su (n)\) spin torus.https://zbmath.org/1456.822672021-04-16T16:22:00+00:00"Hao, Kun"https://zbmath.org/authors/?q=ai:hao.kun"Cao, Junpeng"https://zbmath.org/authors/?q=ai:cao.junpeng"Li, Guang-Liang"https://zbmath.org/authors/?q=ai:li.guangliang"Yang, Wen-Li"https://zbmath.org/authors/?q=ai:yang.wenli"Shi, Kangjie"https://zbmath.org/authors/?q=ai:shi.kangjie"Wang, Yupeng"https://zbmath.org/authors/?q=ai:wang.yupengFisher-Hartwig determinants, conformal field theory and universality in generalised XX models.https://zbmath.org/1456.822722021-04-16T16:22:00+00:00"Hutchinson, J."https://zbmath.org/authors/?q=ai:hutchinson.j-ciaran|hutchinson.john-m-c|hutchinson.j-wesley|hutchinson.james-r|hutchinson.john-j|hutchinson.john-e|hutchinson.joan-p|hutchinson.john-w|hutchinson.joel|hutchinson.john-r"Jones, N. G."https://zbmath.org/authors/?q=ai:jones.nick-gNotes on non-trivial and logarithmic conformal field theories with \(c = 0\).https://zbmath.org/1456.813762021-04-16T16:22:00+00:00"Flohr, Michael"https://zbmath.org/authors/?q=ai:flohr.michael-a-i"Müller-Lohmann, Annekathrin"https://zbmath.org/authors/?q=ai:muller-lohmann.annekathrinFrom Hagedorn to Lee-Yang: partition functions of \(\mathcal{N} = 4\) SYM theory at finite \(N\).https://zbmath.org/1456.814372021-04-16T16:22:00+00:00"Kristensson, Alexander T."https://zbmath.org/authors/?q=ai:kristensson.alexander-t"Wilhelm, Matthias"https://zbmath.org/authors/?q=ai:wilhelm.matthiasSummary: We study the thermodynamics of the maximally supersymmetric Yang-Mills theory with gauge group \(\mathrm{U}(N\)) on \(\mathbb{R} \times S^3\), dual to type IIB superstring theory on \(\mathrm{AdS}_5 \times S^5\). While both theories are well-known to exhibit Hagedorn behavior at infinite \(N\), we find evidence that this is replaced by Lee-Yang behavior at large but finite \(N\): the zeros of the partition function condense into two arcs in the complex temperature plane that pinch the real axis at the temperature of the confinement-deconfinement transition. Concretely, we demonstrate this for the free theory via exact calculations of the (unrefined and refined) partition functions at \(N \leq 7\) for the \(\mathfrak{su} (2)\) sector containing two complex scalars, as well as at \(N \leq 5 \) for the \(\mathfrak{su} (2|3)\) sector containing 3 complex scalars and 2 fermions. In order to obtain these explicit results, we use a Molien-Weyl formula for arbitrary field content, utilizing the equivalence of the partition function with what is known to mathematicians as the Poincaré series of trace algebras of generic matrices. Via this Molien-Weyl formula, we also generate exact results for larger sectors.A general CFT model for antiferromagnetic spin-1/2 ladders with Mobius boundary conditions.https://zbmath.org/1456.821092021-04-16T16:22:00+00:00"Cristofano, Gerardo"https://zbmath.org/authors/?q=ai:cristofano.gerardo"Marotta, Vincenzo"https://zbmath.org/authors/?q=ai:marotta.vincenzo-e"Naddeo, Adele"https://zbmath.org/authors/?q=ai:naddeo.adele"Niccoli, Giuliano"https://zbmath.org/authors/?q=ai:niccoli.giulianoConformal group theory of tensor structures.https://zbmath.org/1456.813562021-04-16T16:22:00+00:00"Burić, Ilija"https://zbmath.org/authors/?q=ai:buric.ilija"Schomerus, Volker"https://zbmath.org/authors/?q=ai:schomerus.volker"Isachenkov, Mikhail"https://zbmath.org/authors/?q=ai:isachenkov.mikhailSummary: The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are functions of cross ratios only, and the correlation functions that depend on insertion points in the \(d\)-dimensional Euclidean space. Here we develop an entirely group theoretic approach to tensor structures, based on the Cartan decomposition of the conformal group. It provides us with a new universal formula for tensor structures and thereby a systematic derivation of crossing equations. Our approach applies to a `gauge' in which the conformal blocks are wave functions of Calogero-Sutherland models rather than solutions of the more standard Casimir equations. Through this ab initio construction of tensor structures we complete the Calogero-Sutherland approach to conformal correlators, at least for four-point functions of local operators in non-supersymmetric models. An extension to defects and superconformal symmetry is possible.Quantum spin Hamiltonians for the \(\mathrm{SU}((2)_k\) WZW model.https://zbmath.org/1456.813932021-04-16T16:22:00+00:00"Nielsen, Anne E. B."https://zbmath.org/authors/?q=ai:nielsen.anne-e-b"Cirac, J. Ignacio"https://zbmath.org/authors/?q=ai:ignacio-cirac.j"Sierra, Germán"https://zbmath.org/authors/?q=ai:sierra.germanNon-simply-connected symmetries in 6D SCFTs.https://zbmath.org/1456.814272021-04-16T16:22:00+00:00"Dierigl, Markus"https://zbmath.org/authors/?q=ai:dierigl.markus"Oehlmann, Paul-Konstantin"https://zbmath.org/authors/?q=ai:oehlmann.paul-konstantin"Ruehle, Fabian"https://zbmath.org/authors/?q=ai:ruehle.fabianSummary: Six-dimensional \(\mathcal{N} = (1, 0)\) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.On the impact of Majorana masses in gravity-matter systems.https://zbmath.org/1456.830192021-04-16T16:22:00+00:00"de Brito, Gustavo P."https://zbmath.org/authors/?q=ai:de-brito.gustavo-p"Hamada, Yuta"https://zbmath.org/authors/?q=ai:hamada.yuta"Pereira, Antonio D."https://zbmath.org/authors/?q=ai:pereira.antonio-d"Yamada, Masatoshi"https://zbmath.org/authors/?q=ai:yamada.masatoshiAn asymptotically safe quantum theory of gravity goes beyond the standard perturbative paradigm. It relies on the existence of a non-trivial UV fixed point that features finitely many relevant directions, corresponding to the number of free parameters to be fixed by experiments. Within this scenario, coupling Standard Model matter degrees to quantum gravity, recent works have managed to explain observed quantities in the low energy regimes by assuming the existence of an asymptotically safe fixed point. In the present work, using the functional renormalization group, the authors ``aim at giving the first steps to investigate the quantum-gravity fluctuations effects to the seesaw mechanism'' -- a mechanism grounded on the introduction of a right-handed neutrino with a Majorana mass term which couples to the left-handed neutrino and the Higgs through a Yukawa interaction. It is worked ``within a specific truncation for the effective average action and with particular choices for gauge parameters, regulators and field parametrizations''. The main findings concern quantum gravity effects on the running of the Majorana masses and the impact of Majorana masses on the running of the Higgs-Majorana couplings. The authors state: ``The system considered in this paper can be regarded as a toy model motivated by neutrino physics.''
Reviewer: Horst-Heino von Borzeszkowski (Berlin)Chaos from massive deformations of Yang-Mills matrix models.https://zbmath.org/1456.813302021-04-16T16:22:00+00:00"Başkan, K."https://zbmath.org/authors/?q=ai:baskan.k"Kürkçüoğlu, S."https://zbmath.org/authors/?q=ai:kurkcuoglu.seckin-kin"Oktay, O."https://zbmath.org/authors/?q=ai:oktay.onur"Taşcı, C."https://zbmath.org/authors/?q=ai:tasci.cSummary: We focus on an \(\mathrm{SU} (N)\) Yang-Mills gauge theory in 0 + 1-dimensions with the same matrix content as the bosonic part of the BFSS matrix model, but with mass deformation terms breaking the global SO(9) symmetry of the latter to \(\mathrm{SO} (5) \times \mathrm{SO}(3) \times \mathbb{Z}_2\). Introducing an ansatz configuration involving fuzzy four- and two-spheres with collective time dependence, we examine the chaotic dynamics in a family of effective Lagrangians obtained by tracing over the aforementioned ansatz configurations at the matrix levels \(N=\frac{1}{6} (n + 1)(n + 2)(n + 3)\), for \(n = 1, 2, \dots , 7\). Through numerical work, we determine the Lyapunov spectrum and analyze how the largest Lyapunov exponents (LLE) change as a function of the energy, and discuss how our results can be used to model the temperature dependence of the LLEs and put upper bounds on the temperature above which LLE values comply with the Maldacena-Shenker-Stanford (MSS) bound \(2 \pi T\), and below which it will eventually be violated.Propagators, BCFW recursion and new scattering equations at one loop.https://zbmath.org/1456.814522021-04-16T16:22:00+00:00"Farrow, Joseph A."https://zbmath.org/authors/?q=ai:farrow.joseph-a"Geyer, Yvonne"https://zbmath.org/authors/?q=ai:geyer.yvonne"Lipstein, Arthur E."https://zbmath.org/authors/?q=ai:lipstein.arthur-e"Monteiro, Ricardo"https://zbmath.org/authors/?q=ai:monteiro.ricardo"Stark-Muchão, Ricardo"https://zbmath.org/authors/?q=ai:stark-muchao.ricardoSummary: We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the \(D\)-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the `linear'-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.Bilinear expansions of lattices of KP \textbf{\( \tau \)}-functions in BKP \textbf{\( \tau \)}-functions: a fermionic approach.https://zbmath.org/1456.813042021-04-16T16:22:00+00:00"Harnad, J."https://zbmath.org/authors/?q=ai:harnad.john"Orlov, A. Yu."https://zbmath.org/authors/?q=ai:orlov.aleksandr-yuSummary: We derive a bilinear expansion expressing elements of a lattice of Kadomtsev-Petviashvili (KP) \( \tau \)-functions, labeled by partitions, as a sum over products of pairs of elements of an associated lattice of BKP \(\tau \)-functions, labeled by strict partitions. This generalizes earlier results relating determinants and Pfaffians of minors of skew symmetric matrices, with applications to Schur functions and Schur \(Q\)-functions. It is deduced using the representations of KP and BKP \(\tau \)-functions as vacuum expectation values (VEVs) of products of fermionic operators of charged and neutral type, respectively. The lattice is generated by the insertion of products of pairs of charged creation and annihilation operators. The result follows from expanding the product as a sum of monomials in the neutral fermionic generators and applying a factorization theorem for VEVs of products of operators in the mutually commuting subalgebras. Applications include the case of inhomogeneous polynomial \(\tau \)-functions of KP and BKP type.
{\copyright 2021 American Institute of Physics}Interface conformal anomalies.https://zbmath.org/1456.813822021-04-16T16:22:00+00:00"Herzog, Christopher P."https://zbmath.org/authors/?q=ai:herzog.christopher-p"Huang, Kuo-Wei"https://zbmath.org/authors/?q=ai:huang.kuo-wei"Vassilevich, Dmitri V."https://zbmath.org/authors/?q=ai:vassilevich.dmitri-vSummary: We consider two \(d \geq 2\) conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we compute the heat kernel coefficients and interface central charges in free theories. The results are consistent with the known boundary CFT data via the folding trick. In \(d = 4\), two interface invariants generally allowed as anomalies turn out to have vanishing interface charges. These missing invariants are constructed from components with odd parity with respect to flipping the orientation of the defect. We conjecture that all invariants constructed from components with odd parity may have vanishing coefficient for symmetric interfaces, even in the case of interacting interface CFT.Generalized dualities and higher derivatives.https://zbmath.org/1456.830932021-04-16T16:22:00+00:00"Codina, Tomas"https://zbmath.org/authors/?q=ai:codina.tomas"Marqués, Diego"https://zbmath.org/authors/?q=ai:marques.diegoSummary: Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local \(O(d,d)\) transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to generalized dualities. Our main result is a unified expression that can be easily specified to any generalized T-duality (abelian, non-abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation (bosonic, heterotic strings and HSZ theory), in any supergravity scheme related by field redefinitions. The prescription allows further extensions to higher orders. As a check we recover some previously known particular examples.Quantum extremal islands made easy. I: Entanglement on the brane.https://zbmath.org/1456.813322021-04-16T16:22:00+00:00"Chen, Hong Zhe"https://zbmath.org/authors/?q=ai:chen.hong-zhe"Myers, Robert C."https://zbmath.org/authors/?q=ai:myers.robert-c"Neuenfeld, Dominik"https://zbmath.org/authors/?q=ai:neuenfeld.dominik"Reyes, Ignacio A."https://zbmath.org/authors/?q=ai:reyes.ignacio-a"Sandor, Joshua"https://zbmath.org/authors/?q=ai:sandor.joshuaSummary: Recent progress in our understanding of the black hole information paradox has lead to a new prescription for calculating entanglement entropies, which involves special subsystems in regions where gravity is dynamical, called \textit{quantum extremal islands}. We present a simple holographic framework where the emergence of quantum extremal islands can be understood in terms of the standard Ryu-Takayanagi prescription, used for calculating entanglement entropies in the boundary theory. Our setup describes a \(d\)-dimensional boundary CFT coupled to a \((d -1)\)-dimensional defect, which are dual to global \(\mathrm{AdS}_{d+1}\) containing a codimension-one brane. Through the Randall-Sundrum mechanism, graviton modes become localized at the brane, and in a certain parameter regime, an effective description of the brane is given by Einstein gravity on an \(\mathrm{AdS}_d\) background coupled to two copies of the boundary CFT. Within this effective description, the standard RT formula implies the existence of quantum extremal islands in the gravitating region, whenever the RT surface crosses the brane. This indicates that islands are a universal feature of effective theories of gravity and need not be tied to the presence of black holes.Graviton-mediated scattering amplitudes from the quantum effective action.https://zbmath.org/1456.830222021-04-16T16:22:00+00:00"Draper, Tom"https://zbmath.org/authors/?q=ai:draper.tom"Knorr, Benjamin"https://zbmath.org/authors/?q=ai:knorr.benjamin"Ripken, Chris"https://zbmath.org/authors/?q=ai:ripken.chris"Saueressig, Frank"https://zbmath.org/authors/?q=ai:saueressig.frankSummary: We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety.A nonabelian M5 brane Lagrangian in a supergravity background.https://zbmath.org/1456.831142021-04-16T16:22:00+00:00"Gustavsson, Andreas"https://zbmath.org/authors/?q=ai:gustavsson.andreasSummary: We present a nonabelian Lagrangian that appears to have \((2, 0)\) superconformal symmetry and that can be coupled to a supergravity background. But for our construction to work, we have to break this superconformal symmetry by imposing as a constraint on top of the Lagrangian that the fields have vanishing Lie derivatives along a Killing direction.Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions.https://zbmath.org/1456.813812021-04-16T16:22:00+00:00"Henkel, Malte"https://zbmath.org/authors/?q=ai:henkel.malte"Stoimenov, Stoimen"https://zbmath.org/authors/?q=ai:stoimenov.stoimenGravitational dual of averaged free CFT's over the Narain lattice.https://zbmath.org/1456.830302021-04-16T16:22:00+00:00"Pérez, Alfredo"https://zbmath.org/authors/?q=ai:perez.alfredo"Troncoso, Ricardo"https://zbmath.org/authors/?q=ai:troncoso.ricardoSummary: It has been recently argued that the averaging of free CFT's over the Narain lattice can be holographically described through a Chern-Simons theory for \( \mathrm{U} (1)^D \times \mathrm{U}(1)^D\) with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT's would be provided by Einstein gravity on \( \mathrm{AdS}_3\) with \( \mathrm{U} (1)^{ D - 1}\times \mathrm{ U} (1)^{ D- 1}\) gauge fields, endowed with a precise set of boundary conditions closely related to the ``soft hairy'' ones. Gravitational excitations then go along diagonal \( \mathrm{SL} (2, \mathbb{R})\) generators, so that the asymptotic symmetries are spanned by \( \mathrm{U} (1)^D \times \mathrm{U} (1)^D\) currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of \( \mathrm{SL} (2, \mathbb{R}) \times \mathrm{U} (1)^{ D- 1}\) generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.Covert symmetry breaking.https://zbmath.org/1456.813332021-04-16T16:22:00+00:00"Erickson, C. W."https://zbmath.org/authors/?q=ai:erickson.c-w"Harrold, A. D."https://zbmath.org/authors/?q=ai:harrold.a-d"Leung, Rahim"https://zbmath.org/authors/?q=ai:leung.rahim"Stelle, K. S."https://zbmath.org/authors/?q=ai:stelle.kellogg-sSummary: Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed `covert' form of spontaneous symmetry breaking can occur, revealing itself only at fourth order in the lower-dimensional effective field theory action. This phenomenon is explored in a simple model of \((d + 1)\)-dimensional scalar QED with one dimension restricted to an interval with Dirichlet/Robin boundary conditions on opposing ends. This produces an effective \(d\)-dimensional theory with Maxwellian dynamics at the free theory level, but with unusual symmetry breaking appearing in the quartic vector-scalar interaction terms. This simple model is chosen to illuminate the mechanism of effects which are also noted in gravitational braneworld scenarios.Quantum spacetime and the universe at the big bang, vanishing interactions and fading degrees of freedom.https://zbmath.org/1456.814472021-04-16T16:22:00+00:00"Doplicher, Sergio"https://zbmath.org/authors/?q=ai:doplicher.sergio"Morsella, Gerardo"https://zbmath.org/authors/?q=ai:morsella.gerardo"Pinamonti, Nicola"https://zbmath.org/authors/?q=ai:pinamonti.nicolaSummary: As discussed in \textit{D. Bahns}, the 1st author et al. [Brunetti, Romeo (ed.) et al., Advances in algebraic quantum field theory. Cham: Springer (ISBN 978-3-319-21352-1/hbk; 978-3-319-21353-8/ebook). Mathematical Physics Studies, 289-329 (2015; Zbl 1334.81078)] fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a ``quantum point'' becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a ``quantum point'' converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in the 1st author et al. [Commun. Math. Phys. 379, No. 3, 1035-1076 (2020; Zbl 07263743)], of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the \(S\) matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.The legacy of Ken Wilson.https://zbmath.org/1456.810062021-04-16T16:22:00+00:00"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-lStringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra.https://zbmath.org/1456.831012021-04-16T16:22:00+00:00"He, Song"https://zbmath.org/authors/?q=ai:he.song"Li, Zhenjie"https://zbmath.org/authors/?q=ai:li.zhenjie"Raman, Prashanth"https://zbmath.org/authors/?q=ai:raman.prashanth"Zhang, Chi"https://zbmath.org/authors/?q=ai:zhang.chiSummary: Stringy canonical forms are a class of integrals that provide \(\alpha\)'-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type \(A_n\) and \(B_n\) generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite \(\alpha\)', and the configuration space is binary although the \(u\) equations take a more general form than those ``perfect'' ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type \(A_n\) and \(B_n\) integrals, which have perfect \(u\) equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.A T-duality interpretation of the relationship between massive and massless magnonic thermodynamic Bethe ansatz systems.https://zbmath.org/1456.813032021-04-16T16:22:00+00:00"Dorey, Patrick"https://zbmath.org/authors/?q=ai:dorey.patrick-e"Miramontes, J. Luis"https://zbmath.org/authors/?q=ai:miramontes.j-luisOne-loop non-planar anomalous dimensions in super Yang-Mills theory.https://zbmath.org/1456.814412021-04-16T16:22:00+00:00"McLoughlin, Tristan"https://zbmath.org/authors/?q=ai:mcloughlin.tristan"Pereira, Raul"https://zbmath.org/authors/?q=ai:pereira.raul"Spiering, Anne"https://zbmath.org/authors/?q=ai:spiering.anneSummary: We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading \(1/N^2\) corrections to operator dimensions and as an example compute the large \(R\)-charge limit for two-excitation states through subleading order in the \(R\)-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite \(N\) to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite \(N\).Spectral theories and topological strings on del Pezzo geometries.https://zbmath.org/1456.831062021-04-16T16:22:00+00:00"Moriyama, Sanefumi"https://zbmath.org/authors/?q=ai:moriyama.sanefumiSummary: Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of \textit{P. del Pezzo} [Nap. Rend. 24, 212--216 (1885; JFM 17.0514.01)] geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.The sine-Gordon model revisited. I.https://zbmath.org/1456.812482021-04-16T16:22:00+00:00"Niccoli, G."https://zbmath.org/authors/?q=ai:niccoli.giuliano"Teschner, J."https://zbmath.org/authors/?q=ai:teschner.jorgEntanglement entropy in conformal field theory: new results for disconnected regions.https://zbmath.org/1456.813572021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasqualeRemarks on black hole complexity puzzle.https://zbmath.org/1456.830482021-04-16T16:22:00+00:00"Yoshida, Beni"https://zbmath.org/authors/?q=ai:yoshida.beniSummary: Recently a certain conceptual puzzle in the AdS/CFT correspondence, concerning the growth of quantum circuit complexity and the wormhole volume, has been identified by Bouland-Fefferman-Vazirani and Susskind. In this note, we propose a resolution of the puzzle and save the quantum Extended Church-Turing thesis by arguing that there is no computational shortcut in measuring the volume due to gravitational backreaction from bulk observers. A certain strengthening of the firewall puzzle from the computational complexity perspective, as well as its potential resolution, is also presented.Combinatorial aspects of boundary loop models.https://zbmath.org/1456.822752021-04-16T16:22:00+00:00"Jacobsen, Jesper Lykke"https://zbmath.org/authors/?q=ai:jacobsen.jesper-lykke"Saleur, Hubert"https://zbmath.org/authors/?q=ai:saleur.hubertS-duality wall of SQCD from Toda braiding.https://zbmath.org/1456.814382021-04-16T16:22:00+00:00"Le Floch, B."https://zbmath.org/authors/?q=ai:le-floch.brunoSummary: Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional \(\mathcal{N} = 2\) \(\mathrm{SU} (N)\) SQCD with \(2N\) hypermultiplets in terms of fields on the defect, namely three-dimensional \(\mathcal{N} = 2\) SQCD with gauge group \(\mathrm{U}(N -1)\) and \(2N\) flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that \(T[ \mathrm{SU} (N)]\) (the S-duality wall of \(\mathcal{N} = 4\) super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a \(\mathrm{USp}(2N - 2)\) gauge theory; it reduces to known results for \(N = 2\). The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT.A new path description for the \({\mathcal M} (k+1,2k+3)\) models and the dual \({\mathcal Z}_k\) graded parafermions.https://zbmath.org/1456.813872021-04-16T16:22:00+00:00"Jacob, P."https://zbmath.org/authors/?q=ai:jacob.punnoose|jacob.p-r|jacob.pierre-e|jacob.pierre|jacob.p-j|jacob.patrick"Mathieu, P."https://zbmath.org/authors/?q=ai:mathieu.phillipe|mathieu.paulette|mathieu.phillippe|mathieu.philippe|mathieu.pierre|mathieu.pierre.2|mathieu.p-pDynamical response functions in the quantum Ising chain with a boundary.https://zbmath.org/1456.821842021-04-16T16:22:00+00:00"Schuricht, Dirk"https://zbmath.org/authors/?q=ai:schuricht.dirk"Essler, Fabian H. L."https://zbmath.org/authors/?q=ai:essler.fabian-h-lUniversal behavior of entanglement in 2D quantum critical dimer models.https://zbmath.org/1456.813862021-04-16T16:22:00+00:00"Hsu, Benjamin"https://zbmath.org/authors/?q=ai:hsu.benjamin-j"Fradkin, Eduardo"https://zbmath.org/authors/?q=ai:fradkin.eduardoCorrections to scaling for block entanglement in massive spin chains.https://zbmath.org/1456.820982021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-l"Peschel, Ingo"https://zbmath.org/authors/?q=ai:peschel.ingoAnalytic results on the geometric entropy for free fields.https://zbmath.org/1456.813012021-04-16T16:22:00+00:00"Casini, H."https://zbmath.org/authors/?q=ai:casini.horacio"Huerta, M."https://zbmath.org/authors/?q=ai:huerta.marinaThe first law of differential entropy and holographic complexity.https://zbmath.org/1456.830842021-04-16T16:22:00+00:00"Sarkar, Debajyoti"https://zbmath.org/authors/?q=ai:sarkar.debajyoti"Visser, Manus"https://zbmath.org/authors/?q=ai:visser.manus-rSummary: We construct the CFT dual of the first law of spherical causal diamonds in three-dimensional AdS spacetime. A spherically symmetric causal diamond in \( \mathrm{AdS}_3\) is the domain of dependence of a spatial circular disk with vanishing extrinsic curvature. The bulk first law relates the variations of the area of the boundary of the disk, the spatial volume of the disk, the cosmological constant and the matter Hamiltonian. In this paper we specialize to first-order metric variations from pure AdS to the conical defect spacetime, and the bulk first law is derived following a coordinate based approach. The AdS/CFT dictionary connects the area of the boundary of the disk to the differential entropy in \( \mathrm{CFT}_2\), and assuming the `complexity=volume' conjecture, the volume of the disk is considered to be dual to the complexity of a cutoff CFT. On the CFT side we explicitly compute the differential entropy and holographic complexity for the vacuum state and the excited state dual to conical AdS using the kinematic space formalism. As a result, the boundary dual of the bulk first law relates the first-order variations of differential entropy and complexity to the variation of the scaling dimension of the excited state, which corresponds to the matter Hamiltonian variation in the bulk. We also include the variation of the central charge with associated chemical potential in the boundary first law. Finally, we comment on the boundary dual of the first law for the Wheeler-deWitt patch of AdS, and we propose an extension of our CFT first law to higher dimensions.Geometric exponents, SLE and logarithmic minimal models.https://zbmath.org/1456.602162021-04-16T16:22:00+00:00"Saint-Aubin, Yvan"https://zbmath.org/authors/?q=ai:saint-aubin.yvan"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Rasmussen, Jørgen"https://zbmath.org/authors/?q=ai:rasmussen.jorgen-h|rasmussen.jorgen|rasmussen.jorgen-bornLogarithmic corrections to the free energy from sharp corners with angle \(2 \pi \).https://zbmath.org/1456.814042021-04-16T16:22:00+00:00"Stéphan, Jean-Marie"https://zbmath.org/authors/?q=ai:stephan.jean-marie"Dubail, Jérôme"https://zbmath.org/authors/?q=ai:dubail.jeromeDynamic scale anomalous transport in QCD with electromagnetic background.https://zbmath.org/1456.814122021-04-16T16:22:00+00:00"Kawaguchi, Mamiya"https://zbmath.org/authors/?q=ai:kawaguchi.mamiya"Matsuzaki, Shinya"https://zbmath.org/authors/?q=ai:matsuzaki.shinya"Huang, Xu-Guang"https://zbmath.org/authors/?q=ai:huang.xu-guangSummary: We discuss phenomenological implications of the anomalous transport induced by the scale anomaly in QCD coupled to an electromagnetic (EM) field, based on a dilaton effective theory. The scale anomalous current emerges in a way perfectly analogous to the conformal transport current induced in a curved spacetime background, or the Nernst current in Dirac and Weyl semimetals --- both current forms are equivalent by a ``Weyl transformation''. We focus on a spatially homogeneous system of QCD hadron phase, which is expected to be created after the QCD phase transition and thermalization. We find that the EM field can induce a dynamic oscillatory dilaton field which in turn induces the scale anomalous current. As the phenomenological applications, we evaluate the dilepton and diphoton productions induced from the dynamic scale anomalous current, and find that those productions include a characteristic peak structure related to the dynamic oscillatory dilaton, which could be tested in heavy ion collisions. We also briefly discuss the out-of-equilibrium particle production created by a nonadiabatic dilaton oscillation, which happens in a way of the so-called tachyonic preheating mechanism.Anomalous dimensions from thermal AdS partition functions.https://zbmath.org/1456.814132021-04-16T16:22:00+00:00"Kraus, Per"https://zbmath.org/authors/?q=ai:kraus.per"Megas, Stathis"https://zbmath.org/authors/?q=ai:megas.stathis"Sivaramakrishnan, Allic"https://zbmath.org/authors/?q=ai:sivaramakrishnan.allicSummary: We develop an efficient method for computing thermal partition functions of weakly coupled scalar fields in AdS. We consider quartic contact interactions and show how to evaluate the relevant two-loop vacuum diagrams without performing any explicit AdS integration, the key step being the use of Källén-Lehmann type identities. This leads to a simple method for extracting double-trace anomalous dimensions in any spacetime dimension, recovering known first-order results in a streamlined fashion.Entanglement entropy of the long-range Dyson hierarchical model.https://zbmath.org/1456.810842021-04-16T16:22:00+00:00"Pappalardi, Silvia"https://zbmath.org/authors/?q=ai:pappalardi.silvia"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Parisi, Giorgio"https://zbmath.org/authors/?q=ai:parisi.giorgioNonperturbative matching between equal-time and lightcone quantization.https://zbmath.org/1456.813752021-04-16T16:22:00+00:00"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 investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of \(\lambda \varphi^4\) theory in \(d = 2\). We discuss the perturbative matching between bare parameters and the failure of its naive nonperturbative extension. We argue that they are nevertheless the same theory nonperturbatively, and that furthermore the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap. We test this map by using it to compare physical quantities computed using numerical Hamiltonian truncation methods in ET and LC.Universal parity effects in the entanglement entropy of XX chains with open boundary conditions.https://zbmath.org/1456.823932021-04-16T16:22:00+00:00"Fagotti, Maurizio"https://zbmath.org/authors/?q=ai:fagotti.maurizio"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasqualeEnumeration of maps with self-avoiding loops and the \(\mathcal{O}(\mathfrak{n})\) model on random lattices of all topologies.https://zbmath.org/1456.824302021-04-16T16:22:00+00:00"Borot, G."https://zbmath.org/authors/?q=ai:borot.gaetan"Eynard, B."https://zbmath.org/authors/?q=ai:eynard.bertrandQuantum quenches in \(1 + 1\) dimensional conformal field theories.https://zbmath.org/1456.813592021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-lSpin-boson type models analyzed using symmetries.https://zbmath.org/1456.811782021-04-16T16:22:00+00:00"Dam, Thomas Norman"https://zbmath.org/authors/?q=ai:dam.thomas-norman"Møller, Jacob Schach"https://zbmath.org/authors/?q=ai:schach-moller.jacobThis paper is devoted to the investigation of a family of models for a qubit interacting with a bosonic field. The authors consider state space \(\mathbb{C}^2 \otimes\mathcal{F}_b(\mathcal{H})\), where Hilbert space \(\mathcal{H}\) is the state space of a single boson and \(\mathcal{F}_b(\mathcal{H})\) is the corresponding bosonic Fock space; the state space of the qubit is \(\mathbb{C}^2\). In the paper under review the following Hamiltonian is investigated
\[H_\eta(\alpha,f,\omega)= \eta\sigma_z\otimes 1 + 1\otimes d\Gamma(\omega)+\sum\limits_{i=1}^{2n} \alpha_i \left(\sigma_x\otimes \phi (f_i)\right)^i .\]
This operator is parameterized by \(\alpha\in\mathbb{C}^{2n}, f\in\mathcal{H}^{2n}, \eta\in\mathbb{C}\), \(\sigma_x, \sigma_y, \sigma_z\) denote the Pauli matrices, \(\omega\) is self-adjoint on \(\mathcal{H}\) and \(d\Gamma(\omega)\) is the second quantization of \(\omega\).
It is assumed that this Hamiltonian has a special symmetry, called \textit{spin-parity symmetry}. The spin-parity symmetry allows to find the domain of self-adjointness and decompose the Hamiltonian into two fiber operators each defined on Fock space. The authors prove the Hunziker-van Winter-Zhislin (HVZ) theorem for the fiber operators. The HVZ theorem for the fiber operators also gives an HVZ theorem for the full Hamiltonian. It is proved that if ground states exist for the full Hamiltonian, then the bottom of the spectrum is a nondegenerate
eigenvalue. Using this result, the authors single out a particular fiber, which has a ground state if and only if the full Hamiltonian has a ground state. Ground states for the other fiber operator must therefore correspond to excited states. A criterion for the existence of an excited state is also obtained.
Reviewer: Michael Perelmuter (Kyjiw)Non minimal d-type conformal matter compactified on three punctured spheres.https://zbmath.org/1456.814012021-04-16T16:22:00+00:00"Sabag, Evyatar"https://zbmath.org/authors/?q=ai:sabag.evyatarSummary: We study compactifications of \(6d\) non minimal \((D_{p+3} , D_{p+3})\) type conformal matter. These can be described by \(N\) M5-branes probing a \(D_{p+3}\)-type singularity. We derive \(4d\) Lagrangians corresponding to compactifications of such \(6d\) SCFTs on three punctured spheres (trinions) with two maximal punctures and one minimal puncture. The trinion models are described by simple \(\mathcal{N} = 1\) quivers with SU \((2N)\) gauge nodes. We derive the trinion Lagrangians using RG flows between the aforementioned \(6d\) SCFTs with different values of \(p\) and their relations to matching RG flows in their compactifications to \(4d\). The suggested trinions are shown to reduce to known models in the minimal case of \(N = 1\). Additional checks are made to show the new minimal punctures uphold the expected S-duality between models in which we exchange two such punctures. We also show that closing the new minimal puncture leads to expected flux tube models.Two-dimensional spanning webs as \((1, 2)\) logarithmic minimal model.https://zbmath.org/1456.813542021-04-16T16:22:00+00:00"Brankov, J. G."https://zbmath.org/authors/?q=ai:brankov.jordan-g|brankov.jovan-g"Grigorev, S. Y."https://zbmath.org/authors/?q=ai:grigorev.s-y"Priezzhev, V. B."https://zbmath.org/authors/?q=ai:priezzhev.vyacheslav-borisovich"Tipunin, I. Y."https://zbmath.org/authors/?q=ai:tipunin.ilya-yuTopological field theories of 2- and 3-forms in six dimensions.https://zbmath.org/1456.814072021-04-16T16:22:00+00:00"Herfray, Yannick"https://zbmath.org/authors/?q=ai:herfray.yannick"Krasnov, Kirill"https://zbmath.org/authors/?q=ai:krasnov.kirill-vSummary: We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term \(BdC\) but differ in the potential term that is added. The theory \(BdC\) with no potential term is topological -- it describes no propagating degrees of freedom. We show that the theory continues to remain topological when either the \(BBB\) or \(C \hat{C}\) potential term is added. The latter theory can be viewed as a background independent version of the 6-dimensional Hitchin theory, for its critical points are complex or para-complex 6-manifolds, but unlike in Hitchin's construction, one does not need to choose a background cohomology class to define the theory. We also show that the dimensional reduction of the \(C \hat{C}\) theory to three dimensions, when reducing on \(S^{3}\), gives 3D gravity.{
\copyright 2017 American Institute of Physics}Inferring topologies via driving-based generalized synchronization of two-layer networks.https://zbmath.org/1456.340642021-04-16T16:22:00+00:00"Wang, Yingfei"https://zbmath.org/authors/?q=ai:wang.yingfei"Wu, Xiaoqun"https://zbmath.org/authors/?q=ai:wu.xiaoqun"Feng, Hui"https://zbmath.org/authors/?q=ai:feng.hui"Lu, Jun-An"https://zbmath.org/authors/?q=ai:lu.junan"Xu, Yuhua"https://zbmath.org/authors/?q=ai:xu.yuhuaAnalysis of the entanglement with centers.https://zbmath.org/1456.814462021-04-16T16:22:00+00:00"Huang, Xing"https://zbmath.org/authors/?q=ai:huang.xing"Ma, Chen-Te"https://zbmath.org/authors/?q=ai:ma.chen-teBTZ one-loop determinants via the Selberg zeta function for general spin.https://zbmath.org/1456.830662021-04-16T16:22:00+00:00"Keeler, Cynthia"https://zbmath.org/authors/?q=ai:keeler.cynthia-a"Martin, Victoria L."https://zbmath.org/authors/?q=ai:martin.victoria-l"Svesko, Andrew"https://zbmath.org/authors/?q=ai:svesko.andrewSummary: We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with \(\mathbb{H}^3/\mathbb{Z}\), extending our work [``Connecting quasinormal modes and heat kernels in 1-loop determinants'', SciPost Phys. 8, No. 2, 017, 22 p. (2020; \url{doi:10.21468/SciPostPhys.8.2.017})]. Previously, \textit{P. A. Perry} and \textit{F. L. Williams} [Int. J. Pure Appl. Math. 9, No. 1, 1--21 (2003; Zbl 1056.11030)] showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.The Baxter \(Q\)-operator for the graded \(\mathrm{SL}(2|1)\) spin chain.https://zbmath.org/1456.812242021-04-16T16:22:00+00:00"Belitsky, A. V."https://zbmath.org/authors/?q=ai:belitsky.andrei-v"Derkachov, S. È."https://zbmath.org/authors/?q=ai:derkachev.sergei-eduardovich"Korchemsky, G. P."https://zbmath.org/authors/?q=ai:korchemsky.gregory-p"Manashov, A. N."https://zbmath.org/authors/?q=ai:manashov.alexander-n\( \mathrm{AdS}_3\) wormholes from a modular bootstrap.https://zbmath.org/1456.830572021-04-16T16:22:00+00:00"Cotler, Jordan"https://zbmath.org/authors/?q=ai:cotler.jordan-s"Jensen, Kristan"https://zbmath.org/authors/?q=ai:jensen.kristanSummary: In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is completely fixed by consistency conditions and a few basic inputs from gravity. This bootstrap is notably for an ensemble of CFTs, rather than for a single instance. We also compare the 3d gravity result with the Narain ensemble. The former is well-approximated at low temperature by a random matrix theory ansatz, and we conjecture that this behavior is generic for an ensemble of CFTs at large central charge with a chaotic spectrum of heavy operators.Logarithmic two-point correlators in the abelian sandpile model.https://zbmath.org/1456.823082021-04-16T16:22:00+00:00"Poghosyan, V. S."https://zbmath.org/authors/?q=ai:poghosyan.vahagn-s"Grigorev, S. Y."https://zbmath.org/authors/?q=ai:grigorev.s-y"Priezzhev, V. B."https://zbmath.org/authors/?q=ai:priezzhev.vyacheslav-borisovich"Ruelle, P."https://zbmath.org/authors/?q=ai:ruelle.philippeOn entanglement Hamiltonians of an interval in massless harmonic chains.https://zbmath.org/1456.813242021-04-16T16:22:00+00:00"Di Giulio, Giuseppe"https://zbmath.org/authors/?q=ai:di-giulio.giuseppe"Tonni, Erik"https://zbmath.org/authors/?q=ai:tonni.erikThermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape.https://zbmath.org/1456.830442021-04-16T16:22:00+00:00"Li, Ran"https://zbmath.org/authors/?q=ai:li.ran"Zhang, Kun"https://zbmath.org/authors/?q=ai:zhang.kun"Wang, Jin"https://zbmath.org/authors/?q=ai:wang.jinSummary: We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.Spin structures and entanglement of two disjoint intervals in conformal field theories.https://zbmath.org/1456.810572021-04-16T16:22:00+00:00"Coser, Andrea"https://zbmath.org/authors/?q=ai:coser.andrea"Tonni, Erik"https://zbmath.org/authors/?q=ai:tonni.erik"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasqualeEffects of non-conformal boundary on entanglement entropy.https://zbmath.org/1456.813052021-04-16T16:22:00+00:00"Loveridge, Andrew"https://zbmath.org/authors/?q=ai:loveridge.andrewSummary: Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but ``mixed'' boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the \(1/N\) corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory.Modular invariance in finite temperature Casimir effect.https://zbmath.org/1456.813482021-04-16T16:22:00+00:00"Alessio, Francesco"https://zbmath.org/authors/?q=ai:alessio.francesco"Barnich, Glenn"https://zbmath.org/authors/?q=ai:barnich.glennSummary: The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell's theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.Nonlocal asymmetric exclusion process on a ring and conformal invariance.https://zbmath.org/1456.822192021-04-16T16:22:00+00:00"Alcaraz, Francisco C."https://zbmath.org/authors/?q=ai:alcaraz.francisco-castilho"Rittenberg, Vladimir"https://zbmath.org/authors/?q=ai:rittenberg.vladimirChiral algebra, localization, modularity, surface defects, and all that.https://zbmath.org/1456.813682021-04-16T16:22:00+00:00"Dedushenko, Mykola"https://zbmath.org/authors/?q=ai:dedushenko.mykola"Fluder, Martin"https://zbmath.org/authors/?q=ai:fluder.martinThe authors study Lagrangian \(\mathcal{N} = 2\) superconformal field theories in four dimensions.
By employing supersymmetric localization on a rigid background of the form \(S^3 \times S^1_y\) they explicitly localize a given Lagrangian superconformal field theory and obtain the corresponding two-dimensional vertex operator algebra VOA (chiral algebra) on the torus \(S^1\times S^1_y\subset S^3\times S^1_y\). To derive the VOA the authors define the appropriate rigid supersymmetric \(S^3 \times S^1_y\) background reproducing the superconformal index. They analyze the supersymmetry algebra and classify the possible fugacities and their preserved subalgebras. Although the minimal amount of supersymmetry needed to retain the VOA construction is \(\mathfrak{su}(1|1)_\ell\times \mathfrak{su}(1|1)_r\) it appears that it is possible to turn on fugacities preserving an \(\mathfrak{su}(1|1)_\ell\times \mathfrak{su}(2|1)_r\) subalgebra which can be further broken to the minimal one by defects. Specifically, discrete fugacities \(M,N \in \mathbb{Z}\) can be turned on. The authors argue that these deformations do not affect the VOA construction but change the complex structure of the
torus and affect the boundary conditions (spin structure) upon going around one of the cycles, \(S^1_y\)
The authors address the two-dimensional theory corresponding to the localization of the \(\mathcal{N} = 2\) vector multiplets and hypermultiplets. In the latter case they show that the remnant classical piece in the localization precisely reduces to the two-dimensional symplectic boson theory on the boundary torus \(S^1\times S^1_y\). The authors show that in the presence of flavor holonomies, which appear as mass-like central charges in the supersymmetry algebra, vertex operators charged under the flavor symmetries fail to remain holomorphic while the sector that remains holomorphic is formed by flavor-neutral operators.
The authors study the modular properties of the four-dimensional Schur index. They introduce formal partition functions \(Z^{(\nu_1,\nu_2)}_{(m,n)}\), which are defined as the partition function in the given spin structure \((\nu_1,\nu_2)\), but with the modified contour of the holonomy integral in the localization formula, labeled by two integers \(m\) and \(n\). The authors suggest that the objects \(Z^{(\nu_1,\nu_2)}_{(m,n)}\) furnish an infinite-dimensional projective representation of \(\mathrm{SL}(2,\mathbb{Z})\).
Finally the authors comment on the flat \(\Omega\)-background underlying the chiral algebra.
Reviewer: Farhang Loran (Isfahan)A boundary matrix for AdS/CFT \(SU(1|1)\) spin chain.https://zbmath.org/1456.821512021-04-16T16:22:00+00:00"Lin, Qingyong"https://zbmath.org/authors/?q=ai:lin.qingyong"Li, Guangliang"https://zbmath.org/authors/?q=ai:li.guangliang"Huang, Yufei"https://zbmath.org/authors/?q=ai:huang.yufeiEntanglement entropy of two disjoint intervals in conformal field theory: II.https://zbmath.org/1456.813612021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-l"Tonni, Erik"https://zbmath.org/authors/?q=ai:tonni.erikEnergy gap for Yang-Mills connections. I: Four-dimensional closed Riemannian manifolds.https://zbmath.org/1456.580142021-04-16T16:22:00+00:00"Feehan, Paul M. N."https://zbmath.org/authors/?q=ai:feehan.paul-m-nSummary: We extend an \(L^2\) energy gap result due to \textit{M. Min-Oo} [Compos. Math. 47, 153--163 (1982; Zbl 0519.53042), Theorem 2] and \textit{T. H. Parker} [Commun. Math. Phys. 85, 563--602 (1982; Zbl 0502.53022), Proposition 2.2] for Yang-Mills connections on principal \(G\)-bundles, \(P\), over closed, connected, four-dimensional, oriented, smooth manifolds, \(X\), from the case of positive Riemannian metrics to the more general case of good Riemannian metrics, including metrics that are generic and where the topologies of \(P\) and \(X\) obey certain mild conditions and the compact Lie group, \(G\), is \(\operatorname{SU}(2)\) or \(\operatorname{SO}(3)\).
[For Part II see Zbl 1375.58013.]Semi-classical limit of quantum free energy minimizers for the gravitational Hartree equation.https://zbmath.org/1456.811882021-04-16T16:22:00+00:00"Choi, Woocheol"https://zbmath.org/authors/?q=ai:choi.woocheol"Hong, Younghun"https://zbmath.org/authors/?q=ai:hong.younghun"Seok, Jinmyoung"https://zbmath.org/authors/?q=ai:seok.jinmyoungThe authors consider the gravitational Vlasov-Poisson equation for a plasma in a gravitational field. They assume that their approach would be valid for large complexes of stars like white dwarfs with a number of stars $N>10^8$ or $N>10^{14}$ for giant stars. The main idea of the actual article is as follows. There is a number of research in which one construct free energy minimizers under some mass constrains.
From an another hand there are also researches which investigate free energy minimizers for the quantum problem, based on the well known Hartree-Fock mean field method.
The problem which is solved by the authors of the actual article concerns with the correspondence between quantum and classical isotropic states. The authors prove some theorems stating that in the limit of very small quantum Planck constant ( when the Planck constant is going to 0), the free energy minimizers for the Hartree-Fock equation converge to those for the Vlasov-Poisson equation in terms of potential functions, as well as via the Wigner transform and the Toplitz quantization.
The authors mention throughout the text of the article an earlier research (1961, 1962) by V.A. Antonov, which is proving the stability of the Vlasov-Poisson equation, applied for stellar many-bodies systems with large number of components. Let us mention, that the famous paper by A.A. Vlasov which established a new kinetic equation for plasma was published in 1938 and only much later was recognized as a correct equation for plasma. See, about this the book by \textit{I. P. Bazarov}, and \textit{P. N. Nikolaev} [Anatolij Aleksandrovich Vlasov ( in Russian), 2nd edition, 63 p. (1999; \url{http:// phys.msu.ru/upload/iblock/0cc/ vlasov-book.pdf})].
Reviewer: Alex B. Gaina (Chisinau)A renormalization group for the truncated conformal space approach.https://zbmath.org/1456.813152021-04-16T16:22:00+00:00"Feverati, G."https://zbmath.org/authors/?q=ai:feverati.giovanni"Graham, K."https://zbmath.org/authors/?q=ai:graham.keith-d|graham.karen-geuther"Pearce, P. A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Tóth, G. Zs."https://zbmath.org/authors/?q=ai:toth.gabor-zsolt"Watts, G. M. T."https://zbmath.org/authors/?q=ai:watts.gerard-m-tStrong coupling expansion of circular Wilson loops and string theories in \(\mathrm{AdS}_5 \times S^5\) and \(\mathrm{AdS}_4 \times CP^3\).https://zbmath.org/1456.831002021-04-16T16:22:00+00:00"Giombi, Simone"https://zbmath.org/authors/?q=ai:giombi.simone"Tseytlin, Arkady A."https://zbmath.org/authors/?q=ai:tseytlin.arkady-aSummary: We revisit the problem of matching the strong coupling expansion of the \(\frac{1}{2}\) BPS circular Wilson loops in \(\mathcal{N} = 4\) SYM and ABJM gauge theories with their string theory duals in \(\mathrm{AdS}_5 \times S^5\) and \(\mathrm{AdS}_4 \times CP^3\), at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor \(1/g_s\) of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension \(T\), both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the \(\sqrt{T}\) prefactor based on special features of the combination of one-loop determinants appearing in the string partition function. The latter also implies a natural generalization \(Z_\chi \sim ( \sqrt{T}/{g}_{s} )^\chi\) to higher genus contributions with the Euler number \(\chi\), which is consistent with the structure of the \(1/N\) corrections found on the gauge theory side.Entanglement entropy of two disjoint intervals in conformal field theory.https://zbmath.org/1456.813602021-04-16T16:22:00+00:00"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasquale"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-l"Tonni, Erik"https://zbmath.org/authors/?q=ai:tonni.erikEstablishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions.https://zbmath.org/1456.830262021-04-16T16:22:00+00:00"Jian, Chao-Ming"https://zbmath.org/authors/?q=ai:jian.chao-ming"Ludwig, Andreas W. W."https://zbmath.org/authors/?q=ai:ludwig.andreas-w-w"Luo, Zhu-Xi"https://zbmath.org/authors/?q=ai:luo.zhu-xi"Sun, Hao-Yu"https://zbmath.org/authors/?q=ai:sun.hao-yu"Wang, Zhenghan"https://zbmath.org/authors/?q=ai:wang.zhenghanSummary: We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius \(l\) is of the order of the Planck scale. Specifically, when the Brown-Henneaux central charge \(c = 3 l/ 2G_N\), (\(G_N\) is the 3D Newton constant) equals \(c = 1/2\), we establish duality between 3D gravity and 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. This duality was suggested by a genus-one calculation of \textit{A. Castro} et al. [``Gravity dual of the Ising model'', Phys. Rev. D 85, No. 2, Article ID 024032, 22 p. (2012; \url{doi:10.1103/PhysRevD.85.024032})]. Extension beyond genus-one requires new mathematical results based on 3D Topological Quantum Field Theory; these turn out to uniquely select the \(c = 1/2\) theory among all those with \textit{c <} 1, extending the previous results of Castro et al. Previous work suggests the reduction of the calculation of the gravity partition function to a problem of summation over the orbits of the mapping class group action on a ``vacuum seed''. But whether or not the summation is well-defined for the general case was unknown before this work. Amongst all theories with Brown-Henneaux central charge \(c < 1\), the sum is finite and unique \textit{only} when \(c = 1/2\), corresponding to a dual Ising conformal field theory on the asymptotic boundary.Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions.https://zbmath.org/1456.814162021-04-16T16:22:00+00:00"Squarcini, A."https://zbmath.org/authors/?q=ai:squarcini.alessio"Maciołek, A."https://zbmath.org/authors/?q=ai:maciolek.a"Eisenriegler, E."https://zbmath.org/authors/?q=ai:eisenriegler.erich"Dietrich, S."https://zbmath.org/authors/?q=ai:dietrich.sarah-m|dietrich.sven|dietrich.sascha|dietrich.stefan|dietrich.suzanne-wBose-Fermi duality and entanglement entropies.https://zbmath.org/1456.810692021-04-16T16:22:00+00:00"Headrick, Matthew"https://zbmath.org/authors/?q=ai:headrick.matthew"Lawrence, Albion"https://zbmath.org/authors/?q=ai:lawrence.albion"Roberts, Matthew"https://zbmath.org/authors/?q=ai:roberts.matthew-mPhysical combinatorics and quasiparticles.https://zbmath.org/1456.822552021-04-16T16:22:00+00:00"Feverati, Giovanni"https://zbmath.org/authors/?q=ai:feverati.giovanni"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Witte, Nicholas S."https://zbmath.org/authors/?q=ai:witte.nicholas-sQuench dynamics of a Tonks-Girardeau gas released from a harmonic trap.https://zbmath.org/1456.825812021-04-16T16:22:00+00:00"Collura, Mario"https://zbmath.org/authors/?q=ai:collura.mario"Sotiriadis, Spyros"https://zbmath.org/authors/?q=ai:sotiriadis.spyros"Calabrese, Pasquale"https://zbmath.org/authors/?q=ai:calabrese.pasqualeAn application of cubical cohomology to Adinkras and supersymmetry representations.https://zbmath.org/1456.814292021-04-16T16:22:00+00:00"Doran, Charles F."https://zbmath.org/authors/?q=ai:doran.charles-f"Iga, Kevin M."https://zbmath.org/authors/?q=ai:iga.kevin-m"Landweber, Gregory D."https://zbmath.org/authors/?q=ai:landweber.gregory-dSummary: An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincaré algebra. The markings on the vertices and edges of an Adinkra are cochains for cubical cohomology. This article explores the cubical cohomology of Adinkras, treating these markings analogously to characteristic classes on smooth manifolds.The Baxter Q operator of critical dense polymers.https://zbmath.org/1456.823052021-04-16T16:22:00+00:00"Nigro, Alessandro"https://zbmath.org/authors/?q=ai:nigro.alessandroIntegrals of motion for critical dense polymers and symplectic fermions.https://zbmath.org/1456.813942021-04-16T16:22:00+00:00"Nigro, Alessandro"https://zbmath.org/authors/?q=ai:nigro.alessandroM-theory and orientifolds.https://zbmath.org/1456.140462021-04-16T16:22:00+00:00"Braun, Andreas P."https://zbmath.org/authors/?q=ai:braun.andreas-pSummary: We construct the M-Theory lifts of type IIA orientifolds based on \(K3\)-fibred Calabi-Yau threefolds with compatible involutions. Such orientifolds are shown to lift to M-Theory on twisted connected sum \(G_2\) manifolds. Beautifully, the two building blocks forming the \(G_2\) manifold correspond to the open and closed string sectors. As an application, we show how to use such lifts to explicitly study open string moduli. Finally, we use our analysis to construct examples of \(G_2\) manifolds with different inequivalent TCS realizations.Statistical mechanics of logarithmic REM: duality, freezing and extreme value statistics of 1/f noises generated by Gaussian free fields.https://zbmath.org/1456.825012021-04-16T16:22:00+00:00"Fyodorov, Yan V."https://zbmath.org/authors/?q=ai:fyodorov.yan-v"Le Doussal, Pierre"https://zbmath.org/authors/?q=ai:le-doussal.pierre"Rosso, Alberto"https://zbmath.org/authors/?q=ai:rosso.albertoThermodynamics of the quantum \(su(1, 1)\) Landau-Lifshitz model.https://zbmath.org/1456.822972021-04-16T16:22:00+00:00"Melikyan, A."https://zbmath.org/authors/?q=ai:melikyan.arsen"Pinzul, A."https://zbmath.org/authors/?q=ai:pinzul.aleksandrMatrix model description of Laughlin Hall states.https://zbmath.org/1456.814822021-04-16T16:22:00+00:00"Cappelli, Andrea"https://zbmath.org/authors/?q=ai:cappelli.andrea"Riccardi, Mauro"https://zbmath.org/authors/?q=ai:riccardi.mauroGeneral solution of an exact correlation function factorization in conformal field theory.https://zbmath.org/1456.814022021-04-16T16:22:00+00:00"Simmons, Jacob J. H."https://zbmath.org/authors/?q=ai:simmons.jacob-j-h"Kleban, Peter"https://zbmath.org/authors/?q=ai:kleban.peterEuclidean black saddles and \(\mathrm{AdS}_4\) black holes.https://zbmath.org/1456.830382021-04-16T16:22:00+00:00"Bobev, Nikolay"https://zbmath.org/authors/?q=ai:bobev.nokolai"Charles, Anthony M."https://zbmath.org/authors/?q=ai:charles.anthony-m"Min, Vincent S."https://zbmath.org/authors/?q=ai:min.vincent-sSummary: We find new asymptotically locally \(\mathrm{AdS}_4\) Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These ``black saddles'' have an \(S^1 \times {\Sigma}_{\mathfrak{g}}\) boundary at asymptotic infinity and cap off smoothly in the interior. The solutions can be uplifted to eleven dimensions and are holographically dual to the topologically twisted ABJM theory on \(S^1 \times {\Sigma}_{\mathfrak{g}}\). We show explicitly that the on-shell action of the black saddle solutions agrees exactly with the topologically twisted index of the ABJM theory in the planar limit for general values of the magnetic fluxes, flavor fugacities, and real masses. This agreement relies on a careful holographic renormalization analysis combined with a novel UV/IR holographic relation between supergravity parameters and field theory sources. The Euclidean black saddle solution space contains special points that can be Wick-rotated to regular Lorentzian supergravity backgrounds that correspond to the well-known supersymmetric dyonic \(\mathrm{AdS}_4\) black holes in the STU model.Boundary states, overlaps, nesting and bootstrapping AdS/dCFT.https://zbmath.org/1456.812342021-04-16T16:22:00+00:00"Gombor, Tamas"https://zbmath.org/authors/?q=ai:gombor.tamas"Bajnok, Zoltan"https://zbmath.org/authors/?q=ai:bajnok.zoltanSummary: Integrable boundary states can be built up from pair annihilation amplitudes called \(K\)-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate these two notions to each other and show how they are fixed by the unbroken symmetries, which, together with the full symmetry, must form symmetric pairs. We show that the twisted nature of the \(K\)-matrix implies specific selection rules for the overlaps. If the Bethe roots of the same type are paired the overlap is called chiral, otherwise it is achiral and they correspond to untwisted and twisted \(K\)-matrices, respectively. We use these findings to develop a nesting procedure for \(K\)-matrices, which provides the factorizing overlaps for higher rank algebras automatically. We apply these methods for the calculation of the simplest asymptotic all-loop 1-point functions in AdS/dCFT. In doing so we classify the solutions of the YBE for the \(K\)-matrices with centrally extended \(\mathfrak{su} (2|2)_c\) symmetry and calculate the generic overlaps in terms of Bethe roots and ratio of Gaudin determinants.Linear Batalin-Vilkovisky quantization as a functor of \(\infty \)-categories.https://zbmath.org/1456.180182021-04-16T16:22:00+00:00"Gwilliam, Owen"https://zbmath.org/authors/?q=ai:gwilliam.owen"Haugseng, Rune"https://zbmath.org/authors/?q=ai:haugseng.runeThe authors consider a categorical construction of linear Batalin-Vilkovisky quantization in a derived setting.
The basic example that is the starting point for this article is the Weyl quantization, sending a symplectic vector space \(\mathbb R^{2n}\) to the Weyl algebra on \(2n\) generators. One can factor this construction as taking a vector space with a skew-symmetric form first to its Heisenberg Lie algebra and then to its universal envelopping algebra. The specalization at \(\hbar = 0\) of this universal envelopping algebra is a Poisson algebra and the specializiation at \(\hbar = 1\) is its quantizaiton.
The authors consider a special case of the shifted derived versions of this problem: Their starting point are chain complexes equipped with a 1-shifted symmetric pairing. Following the article we will call them quadratic modules for short.
They then construct \(\infty\)-categorical versions of both the Heisenberg Lie algebra (which is actually a shifted \(L_\infty\)-algebra) of a quadratic module, and the universal enveloping \(BD\)-algebra of a shifted Lie algebra. Both of these appear to be of independent interest.
The universal enveloping \(BD\)-algebra is a so-called Beilinson-Drinfeld algebra, a \(k[\hbar]\)-algebra over a certain operad that specialises to a shifted Poisson algebra at \(\hbar = 0\) and to an \(E_0\)-algebra at \(\hbar = 1\). (An \(E_0\)-algebra is just a pointed chain complex, but this is the correct edge case of the notion of \(E_n\)-algebras. The classical, unshifted case involves an unshifted Poisson algebra and an \(E_1\)-algebra (i.e.\ an associative algebra) as specializiations.)
Thus the authors are able to construct linear BV quantization as a symmetric monoidal \(\infty\)-functor from quadratic algebras to \(BD\)-algebras.
The proofs involve a mixture of categorical techniques (model, simplicial and \(\infty\)).
One upside of the \(\infty\)-categorical approach is that by using Lurie's descent theorem the author can consider linear BV quantization for sheaves of quadratic modules on derived stacks. Thus they are able to show that the graded vector bundle \(V \oplus V^\vee[1]\) with its obvious quadratic form quantizes to a line bundle. This is an explicit example of the BV formalism ``behaving like a determinant'', an idea the authors credit to K. Costello. The paper also provides an example that the behaviour for more general 1-shifted symplectic modules is more complicated and the quantization need only be invertible in the formal neighbourhood of a point.
The paper under review contains some interesting discussions in the introduction: Section 1.3 considers higher BV quantizations (which should arise from more general \((1-n)\)-shifted skew-symmetric forms) and a possible application to quantization of AKSZ field theories. Section 1.4 discusses the physical perspective on linear BV quantizations, providing useful context and motivation.
Reviewer: Julian Holstein (Hamburg)Connecting global and local energy distributions in quantum spin models on a lattice.https://zbmath.org/1456.813202021-04-16T16:22:00+00:00"Arad, Itai"https://zbmath.org/authors/?q=ai:arad.itai"Kuwahara, Tomotaka"https://zbmath.org/authors/?q=ai:kuwahara.tomotaka"Landau, Zeph"https://zbmath.org/authors/?q=ai:landau.zeph-aForm factors of descendant operators in the massive Lee-Yang model.https://zbmath.org/1456.813022021-04-16T16:22:00+00:00"Delfino, Gesualdo"https://zbmath.org/authors/?q=ai:delfino.gesualdo"Niccoli, Giuliano"https://zbmath.org/authors/?q=ai:niccoli.giulianoLogarithmic minimal models.https://zbmath.org/1456.812172021-04-16T16:22:00+00:00"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Rasmussen, Jørgen"https://zbmath.org/authors/?q=ai:rasmussen.jorgen-h|rasmussen.jorgen|rasmussen.jorgen-born"Zuber, Jean-Bernard"https://zbmath.org/authors/?q=ai:zuber.jean-bernardBethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory.https://zbmath.org/1456.812412021-04-16T16:22:00+00:00"Kormos, M."https://zbmath.org/authors/?q=ai:kormos.marton"Mussardo, G."https://zbmath.org/authors/?q=ai:mussardo.guiseppe|mussardo.giuseppe"Pozsgay, B."https://zbmath.org/authors/?q=ai:pozsgay.balazsRigorous analysis of the Tomonaga model by means of Ward identities and the renormalization group.https://zbmath.org/1456.823992021-04-16T16:22:00+00:00"Benfatto, Giuseppe"https://zbmath.org/authors/?q=ai:benfatto.giuseppe"Mastropietro, Vieri"https://zbmath.org/authors/?q=ai:mastropietro.vieriCovariant representations for possibly singular actions on \(C^*\)-algebras.https://zbmath.org/1456.460552021-04-16T16:22:00+00:00"Beltiţă, Daniel"https://zbmath.org/authors/?q=ai:beltita.daniel"Grundling, Hendrik"https://zbmath.org/authors/?q=ai:grundling.hendrik-b|grundling.hendrik-b-g-s"Neeb, Karl-Hermann"https://zbmath.org/authors/?q=ai:neeb.karl-hermannSummary: Singular actions on \(C^*\)-algebras are automorphic group actions on \(C^*\)-algebras, where the group is not locally compact, or the action is not strongly continuous. We study the covariant representation theory of actions which may be singular. In the usual case of strongly continuous actions of locally compact groups on \(C^*\)-algebras, this is done via crossed products, but this approach is not available for singular \(C^*\)-actions. We explored extension of crossed products to singular actions in a previous paper [\textit{H. Grundling} and \textit{K.-H. Neeb}, J. Funct. Anal. 266, No. 8, 5199--5269 (2014; Zbl 1303.46059)]. The literature regarding covariant representations for possibly singular actions is already large and scattered, and in need of some consolidation. We collect in this survey a range of results in this field, mostly known. We improve some proofs and elucidate some interconnections. These include existence theorems by Borchers and Halpern, Arveson spectra, the Borchers-Arveson theorem, standard representations and Stinespring dilations as well as ground states, KMS states and ergodic states and the spatial structure of their GNS representations.Dipolar stochastic Loewner evolutions.https://zbmath.org/1456.827132021-04-16T16:22:00+00:00"Bauer, M."https://zbmath.org/authors/?q=ai:bauer.martin.1|bauer.michael.1|bauer.michael.2|bauer.mariano|bauer.max|bauer.marcus|bauer.marco|bauer.michel|bauer.madeleine|bauer.maria|bauer.michael-a|bauer.mathias|bauer.matthias|bauer.manfred|bauer.martin.2|bauer.martin.3"Bernard, D."https://zbmath.org/authors/?q=ai:bernard.daniel|bernard.damien|bernard.douglas-e|bernard.denis"Houdayer, J."https://zbmath.org/authors/?q=ai:houdayer.jeromeQuench dynamics in two-dimensional integrable SUSY models.https://zbmath.org/1456.814252021-04-16T16:22:00+00:00"Cortés Cubero, Axel"https://zbmath.org/authors/?q=ai:cubero.axel-cortes"Mussardo, Giuseppe"https://zbmath.org/authors/?q=ai:mussardo.giuseppe"Panfil, Miłosz"https://zbmath.org/authors/?q=ai:panfil.miloszFusion hierarchies, \(T\)-systems, and \(Y\)-systems of logarithmic minimal models.https://zbmath.org/1456.813912021-04-16T16:22:00+00:00"Morin-Duchesne, Alexi"https://zbmath.org/authors/?q=ai:morin-duchesne.alexi"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Rasmussen, Jørgen"https://zbmath.org/authors/?q=ai:rasmussen.jorgen-h|rasmussen.jorgen|rasmussen.jorgen-bornOn a gravity dual to flavored topological quantum mechanics.https://zbmath.org/1456.830632021-04-16T16:22:00+00:00"Feldman, Andrey"https://zbmath.org/authors/?q=ai:feldman.andreySummary: In this paper, we propose a generalization of the \(\mathrm{AdS}_2/\mathrm{CFT}_1\) correspondence constructed by \textit{M. Mezei} in [``A 2d/1d holographic duality'', Preprint, \url{arXiv:1703.08749}], which is the duality between 2d Yang-Mills theory with higher derivatives in the \(\mathrm{AdS}_2\) background, and 1d topological quantum mechanics of two adjoint and two fundamental \(\mathrm{U}(N)\) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level \(k = 1\). We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [loc. cit.], which arises as the effective field theory living on the intersection of stacks of \(N\) D2-branes and \(k\) D6-branes in the \(\Omega\)-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in \(\mathcal{N} = 4\) theory with \(k\) fundamental hypermultiplets, having a holographic description as M-theory in the \(\mathrm{AdS}_4 \times S^7/ \mathbb{Z}_k\) background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.Emptiness formation probability, Toeplitz determinants, and conformal field theory.https://zbmath.org/1456.820762021-04-16T16:22:00+00:00"Stéphan, Jean-Marie"https://zbmath.org/authors/?q=ai:stephan.jean-marieHaldane model at finite temperature.https://zbmath.org/1456.813262021-04-16T16:22:00+00:00"Leonforte, Luca"https://zbmath.org/authors/?q=ai:leonforte.luca"Valenti, Davide"https://zbmath.org/authors/?q=ai:valenti.davide"Spagnolo, Bernardo"https://zbmath.org/authors/?q=ai:spagnolo.bernardo"Dubkov, Alexander A."https://zbmath.org/authors/?q=ai:dubkov.alexander-a"Carollo, Angelo"https://zbmath.org/authors/?q=ai:carollo.angelo-c-mA hydrodynamic approach to non-equilibrium conformal field theories.https://zbmath.org/1456.825432021-04-16T16:22:00+00:00"Bernard, Denis"https://zbmath.org/authors/?q=ai:bernard.denis"Doyon, Benjamin"https://zbmath.org/authors/?q=ai:doyon.benjaminDe Sitter in non-supersymmetric string theories: no-go theorems and brane-worlds.https://zbmath.org/1456.830882021-04-16T16:22:00+00:00"Basile, Ivano"https://zbmath.org/authors/?q=ai:basile.ivano"Lanza, Stefano"https://zbmath.org/authors/?q=ai:lanza.stefanoSummary: We study de Sitter configurations in ten-dimensional string models where supersymmetry is either absent or broken at the string scale. To this end, we derive expressions for the cosmological constant in general warped flux compactifications with localized sources, which yield no-go theorems that extend previous works on supersymmetric cases. We frame our results within a dimensional reduction and connect them to a number of Swampland conjectures, corroborating them further in the absence of supersymmetry. Furthermore, we construct a top-down string embedding of de Sitter brane-world cosmologies within unstable anti-de Sitter landscapes, providing a concrete realization of a recently revisited proposal.CFT unitarity and the AdS Cutkosky rules.https://zbmath.org/1456.813902021-04-16T16:22:00+00:00"Meltzer, David"https://zbmath.org/authors/?q=ai:meltzer.david"Sivaramakrishnan, Allic"https://zbmath.org/authors/?q=ai:sivaramakrishnan.allicSummary: We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.Finite-temperature dynamical correlations in massive integrable quantum field theories.https://zbmath.org/1456.812312021-04-16T16:22:00+00:00"Essler, Fabian H. L."https://zbmath.org/authors/?q=ai:essler.fabian-h-l"Konik, Robert M."https://zbmath.org/authors/?q=ai:konik.robert-mThe scaling limit of two cluster boundaries in critical lattice models.https://zbmath.org/1456.813772021-04-16T16:22:00+00:00"Gamsa, Adam"https://zbmath.org/authors/?q=ai:gamsa.adam"Cardy, John"https://zbmath.org/authors/?q=ai:cardy.john-lLogarithmic superconformal minimal models.https://zbmath.org/1456.813962021-04-16T16:22:00+00:00"Pearce, Paul A."https://zbmath.org/authors/?q=ai:pearce.paul-a"Rasmussen, Jørgen"https://zbmath.org/authors/?q=ai:rasmussen.jorgen-born|rasmussen.jorgen-h|rasmussen.jorgen"Tartaglia, Elena"https://zbmath.org/authors/?q=ai:tartaglia.elenaArithmetic Chern-Simons theory. I.https://zbmath.org/1456.140292021-04-16T16:22:00+00:00"Kim, Minhyong"https://zbmath.org/authors/?q=ai:kim.minhyongSummary: In this paper, we apply ideas of \textit{R. Dijkgraaf} and \textit{E. Witten} [Commun. Math. Phys. 129, No. 2, 393--429 (1990; Zbl 0703.58011)] and \textit{E. Witten} [Commun. Math. Phys. 121, No. 3, 351--399 (1989; Zbl 0667.57005)] on \(2+1\) dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical Chern-Simons functionals on spaces of Galois representations. In the highly speculative Sect. 6, we consider the far-fetched possibility of using Chern-Simons theory to construct \(L\)-functions.
For the entire collection see [Zbl 07237934].