Thermal Seminars - Recordings

Title: OPE=QNM

Abstract: We discuss the analytic structure of holographic thermal correlators at fixed spatial momentum. These correlators admit natural short time (OPE) and large time (QNM) expansions. We show that the two expansions agree in a common domain of convergence in the complex time plane. By comparing the two expansions near singularities in the complex time plane we give a map between OPE and QNM data, and obtain new analytic results for QNM asymptotics. We further show that the OPE spectrum is intimately related to QNM data through a set of sum rules that naturally arise in Mellin space.

Title: Thermal One-point Functions and Asymptotic CFT Data: QFT in AdS

Speaker: Francesco Russo

Based on: 2606.17167

Abstract: We investigate one-point functions of CFTs on S^1 \times S^2 to probe the heavy sector of the theory. We first review strategies to extract asymptotic CFT data, such as Heavy-Heavy-Light OPE coefficients. We then apply this machinery to the CFT dual to a massive scalar field in AdS_4, computing the first-order corrections to the non-interacting bulk theory. This approach allows us to systematically study asymptotic CFT data at both large and fixed particle numbers. (Based on arXiv:2606.17167 with I. Burić, F. Mangialardi, V. Schomerus, and A. Vichi).

Title: Finite temperature quantum systems and black holes

Speaker: Juan Maldacena

Review Talk

Abstract: Black holes can behave as quantum systems at finite temperature. This talk will be a review of this connection. We will talk about thermalization and quasinormal modes, quantum chaos, simple quantum mechanical models, some of the effects associated to the sum over topologies, etc.

Title: Thermal OPE, exact WKB, and the black hole singularity

Speaker: Mukund Rangamani

Based on: 2512.15114, 2604.10803

Abstract: I will discuss analytic properties of thermal spectral functions of holographic CFTs, both at finite and asymptotic values of momenta. For a special class of scalar operators with integer dimensions in even dimensional holographic CFTs, we obtain a full transseries at large timelike momentum. This information, we argue, captures imprints of the black hole singularity in the dual field theory observables. Time permitting, I will also explain universality of these signatures. The talk is based on work with Hewei Frederic Jia.

Title: Towards a consistent perturbation theory at finite temperature

Speaker: Peter Lowdon

Based on: 2606.14863

Abstract: The Gell-Mann-Low relation forms the foundation of all perturbative approaches to QFT. In order to establish how perturbation theory can be consistently generalised to finite-temperature systems it is therefore necessary to understand how this relation is modified by thermal effects. In this talk I will introduce a new proposal for how this relation should be generalised, based on the non-perturbative spectral characteristics of thermal correlation functions. I will outline why the perturbative expansion in this framework resolves the major problems of the standard real-time approach, and using numerical lattice simulations in massive $\phi^{4}$ theory I will demonstrate that this framework provides precise predictions of the lattice data, in contrast to the standard approach.

Title: Complete mode decomposition of Green’s functions and bouncing singularities

Speaker: Paolo Arnaudo

Based on: 2605.16489

Abstract: Quasinormal modes are the characteristic damped oscillations of black holes and are central to the theory of ringdown. However, the quasinormal mode expansion of the retarded Green’s function provides a convergent representation only in a late-time region. In this talk, I will describe how to complete this mode decomposition by including a set of Matsubara modes, which reconstruct the Green’s function in the earlier-time region where the quasinormal mode sum fails. The main focus will be the Schwarzschild case. I will show that the boundary of the quasinormal mode convergence region has a precise geometric origin. It is controlled by singularities of the Green’s function at complex times, produced by null geodesics that bounce from the black-hole singularity. These bouncing singularities determine the radius of convergence of the quasinormal mode sum and explain the otherwise mysterious bounce radius appearing in the complete mode decomposition.

Title: Thermal partition function from the S-matrix reloaded

Speaker: Joan Elias Miró

Based on: 2512.16466

Abstract: Over the past decade, S-matrix-based methods have undergone a remarkable resurgence as elegant and powerful tools for extracting physical information without relying on an underlying Lagrangian formulation. A central question is: given the exact S-matrix of a quantum field theory, what can we learn about its thermodynamic properties? In this talk, I will review the Dashen–Ma–Bernstein formalism, which relates thermodynamics directly to scattering amplitudes. I will illustrate it with the perturbative QCD equation of state and with the effective theory of long confining flux tubes, including non-universal corrections and comparisons with Thermodynamic Bethe Ansatz results. More broadly, these methods offer a way to extract thermodynamic observables directly from on-shell data, with potential applications to EFTs constrained by modern bootstrap and positivity techniques.

Title: Proof of Entropic Order in Generalized Ising Models

Speaker: Enrico Andriolo

Based on: 2604.09768

Abstract: It is commonly expected that increasing temperature drives physical systems towards disorder. Surprisingly, certain models are conjectured to exhibit the opposite behaviour: at extremely high temperatures, they enter an ordered phase stabilized by entropy. After a gentle introduction to this counterintuitive phenomenon, I will outline the main ideas behind a rigorous proof showing that such entropically driven order can indeed occur. I will do so for a class of lattice systems that generalize the usual Ising model. No prior familiarity with the topic will be assumed.

Title: Neural Spectral Bias and Conformal Correlators

Speaker: Andreas Stergiou (Ανδρέας Στεργίου)

Based on: 2604.18673 , 2604.18686

Abstract: Can a simple neural network deduce the full functional form of a conformal field theory (CFT) correlation function from almost nothing? In this talk, I will demonstrate that by training a neural network using only crossing symmetry, correlator asymptotics, and a single “anchor point”, one can successfully recover correlators across a wide range of theories. I will argue that this success is driven by the spectral bias of neural networks, which inherently focuses on maximally smooth functions. This suggests a potential new aspect of CFTs: their correlators are among the smoothest crossing-symmetric functions.

Title: PT-symmetric Field Theories at Finite Temperature

Speaker: Andrei Katsevich (Андрей Коцевич)

Based on: 2604.08459

Abstract: This talk will discuss finite-temperature PT-symmetric scalar field theories with imaginary couplings. I will describe how the free energy, thermal masses, and one-point functions encode information about the corresponding two-dimensional CFTs. To remove infrared divergences, I will introduce a ''thermal normal-ordering'' scheme that resums these contributions and yields a systematic \epsilon-expansion. I will compare the two-dimensional results with exact predictions derived from the proposed Ginzburg-Landau descriptions of the non-unitary minimal models M(2,5) and M(3,8)_D, and use Padé extrapolations to estimate the free energy density in higher dimensions. This talk will discuss finite-temperature PT-symmetric scalar field theories with imaginary couplings. I will describe how the free energy, thermal masses, and one-point functions encode information about the corresponding two-dimensional CFTs. To remove infrared divergences, I will introduce a ''thermal normal-ordering'' scheme that resums these contributions and yields a systematic \epsilon-expansion. I will compare the two-dimensional results with exact predictions derived from the proposed Ginzburg-Landau descriptions of the non-unitary minimal models M(2,5) and M(3,8)_D, and use Padé extrapolations to estimate the free energy density in higher dimensions.

Title: Planckian bound on the local equilibration time

Speaker: Alexey Milekhin

Based on: 2602.17638

Abstract: The local equilibration time t_eq of quantum many-body systems is conjectured to be bounded below by the Planckian time hbar/T. We formalize this conjecture by defining t_eq as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound t_eq >= \alpha hbar/T on the onset of hydrodynamic behavior in a 'regulated' thermal two-point function. The dimensionless coefficient alpha depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.

Title: Finite Temperature Properties of Negative Coupling Scalar Field Theory

Speaker: Paul Romatschke

Based on: 2603.19877

Abstract: Quantum Field Theory is a mature technology that is highly predictive. Most textbooks construct quantum field theory as an expansion for small positive coupling around classically stable vacua, which is a perfectly reasonable thing to do. However, history tells us that quantum mechanics sometimes does not conform to classical intuition. In this talk, I will give arguments why some negative coupling systems nevertheless are stable and physically acceptable quantum mechanically. I fill focus on the finite temperature properties of negative coupling field theory in different dimensions, outlining the similarities and differences with respect to "usual" positive coupling theories.

Title: Thermalization of (1+1)d QFTs at high temperature

Speaker: Richard Davison

Based on: 2512.11024

Abstract: Interacting QFTs typically thermalize, leading to the emergence of hydrodynamics. I will explain how (1+1)d QFTs at large N provide a setting in which this phenomenon is analytically tractable. In particular, I will argue that the thermal two-point function of the stress tensor is universal in the near-lightcone, high-temperature limit of these theories. This universal expression captures of the emergence of a fluid-like state at late times and quantitatively predicts how its properties (e.g. viscosity) are related to the microscopic details of the QFT. i will show that explicit computations in holographic theories are consistent with these predictions.

Title: Holographic thermal correlators from Fourier series

Speaker: Benjamin Withers

Based on: 2603.13469

Abstract: There has been much recent interest in thermal correlators in AdS/CFT, particularly their analytic structure and OPE expansions in relation to black hole singularities and bouncing geodesics. I will discuss a recent computation of the Euclidean correlator expressed as a Fourier series on the thermal circle as a convenient way to directly access and explore these features. The Fourier series does not converge in the sense of functions, but instead converges as a distribution. The result is manifestly periodic in Euclidean time and analytic in the thermal strip. In the OPE limit the result includes both stress-tensor and double-trace OPE sectors, which both correspond to data in the asymptotic expansion of the Fourier coefficients. Bouncing singularities appear as non-perturbative contributions in this asymptotic expansion, but do not contribute to the Euclidean correlator.

Title: High temperature glass and high temperature order

Speaker: Tin Sulejmanpasic

Based on: 2512.07980

Abstract: When you heat things, they melt. This is because the free energy E-TS is minimized by maximizing entropy, as long as temperature is high enough. Since high-entropy states are typically disordered, melting always ensues at sufficiently high temperature. Yet, recently it has come to light that there exist systems that order to arbitrarily high temperatures, invalidating the basic thermodynamic intuition. Such order is called the entropic order. I will discuss some simple models which exhibit such phenomena, and try to obtain insights into what properties are needed for entropic order.

Title: Thermal correlators on the Wilson line and bouncing singularities

Speaker: Simone Giombi

Based on: 2603.11012

Abstract: I will discuss the calculation of the thermal retarded two-point function of the displacement operator on a Wilson line in N=4 SYM theory at strong coupling. This is computed holographically by solving the wave equation for the transverse fluctuations of the dual string worldsheet in the planar AdS black hole background. Similarly to the case of thermal correlators of local operators dual to bulk scalar fields, these defect correlators are found to exhibit bouncing singularities in complex time, which correspond to exponentially suppressed contributions in the high-frequency limit. I will highlight the agreement of two independent approaches to probe the high-frequency regime of the correlators: a WKB analysis that is sensitive to the black hole interior, and an asymptotic OPE analysis based on a near-boundary expansion.

Title: Bulk phase shift and singularity

Speaker: Manuela Kulaxizi

Based on: 2602.06558

Abstract: High-energy scattering of a light particle off a black hole at fixed impact parameter is described by an eikonal phase, which encodes the resulting time delay and angular deflection. This bulk phase shift admits a holographic interpretation as of the thermal momentum-space two-point function of a scalar operator in the CFT in the Regge limit. At small impact parameter, the phase shift acquires an imaginary part signaling inelastic scattering, obscuring the interpretation of time delay and deflection which become complex-valued. However, in a holographic CFT these quantities can also be extracted from the so called bulk-cone singularities of the position space thermal correlator. Extending this analysis to small impact parameters, we find that the position-space correlator develops a singularity precisely when a null geodesic reflects off the black hole singularity and reaches the opposite boundary. This provides a more robust identification of bulk time delay and angular deflection through singularities of position-space correlators.

Title: Imprint of the black hole interior on thermal four-point correlators

Speaker: Joydeep Chakravarty

Based on: 2512.10912

Abstract: We consider correlators smeared against directed wavepackets over a thermal state dual to a single-sided planar AdS black hole. In the large frequency limit, our measurement is simplified using a bulk WKB description. We propose a dictionary that maps the action of smeared boundary operators to flat-space oscillators near an interior bulk point on the thermal state, by analytically continuing late-time operators from the right to the left boundary via an integral transform. Using the dictionary the smeared correlator factorizes to a flat-space like scattering amplitude about the interior event. Our transformed correlators describe local physics in the two-sided black hole interior, while incurring a suppression of O(exp (-beta omega /2) ). These measurements necessitate a non-trivial time ordering of operators living on boundary hyperboloids which are causally connected to the past light cone of the bulk point, as well as on a corresponding future branch.

Title: Regge's Inferno

Speaker: Zohar Komargodski

Based on: 2603.10197

Abstract: We study large-spin operators in CFTs in d>2 spacetime dimensions. The counting of such operators leads to extensive thermodynamic potentials, with the spin related to the effective volume. The resulting equation of state interpolates between a weakly coupled gas at small twist (the Regge/light-cone bootstrap regime) and a fluid-like regime at larger twist. We show that the same equation of state emerges by placing the CFT on suitable pp-wave backgrounds. In these geometries, locality of quantum fields provides a microscopic explanation for extensivity of the thermodynamic potentials. The pp-waves also make the large-spin symmetry structure manifest: we obtain Heisenberg groups in the large-spin limit. The existence of a vacuum state on these pp-waves is equivalent to a new unitarity bound in 3+1 dimensions.

Title: Black Hole States in Quantum Spin Chains

Speaker: Charlotte Kristjansen

Based on: 2512.23432

Abstract: We define a black hole state in a quantum spin chain by studying thermal correlators in holography. Focusing on the Heisenberg model we investigate the thermal and complexity properties of the black hole state by evaluating its entanglement entropy, emptiness formation probability and Krylov complexity.

Title: Semi-universality of CFT entropy at large spin

Speaker: Shiraz Minwalla

Based on: 2512.00158

Abstract: We argue that the entropy of all d dimensional conformal field theories (studied on S^{d-1}) takes a semi- universal scaling form in a suitable high angular momentum limit. We use the AdS/CFT correspondence to test our prediction for strongly coupled N=4 Yang Mills theory, and find that the thermodynamics of this theory simplifies in the predicted manner in this limit, revealing phase transitions between scaling limits of black holes, grey galaxies and the supergravity gas.

Title: A review on entanglement entropy

Speaker: Pasquale Calabrese

Review talk

Abstract: Over a century ago, Erwin Schrödinger described entanglement as “the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.” Yet it is only in the past two decades that the study of quantum entanglement in many-body systems has reached a level of maturity that has fostered an unprecedented cross-fertilization of ideas across disciplines. Concepts originating in quantum information theory now interact deeply with high-energy physics, statistical mechanics, general relativity, condensed matter physics, and beyond. In this colloquium-style thermal seminar, I will present a selection of examples drawn from different areas of physics in which many-body entanglement emerges as the defining physical feature, shaping both the structure of the theory and the observable dynamics of the system.

Title: A genus-2 crossing equation in d≥2

Speaker: Yixin Xu (许伊欣)

Based on: 2511.07569

Abstract: In this talk I’ll describe a new “genus-2” crossing equation obeyed by conformal field theories in any spacetime dimension d≥2. The crossing equation compares two different decompositions of a “genus-2 partition function” – CFT partition function on the connected sum of two S^2 \times S^{d-1}. In the “sunrise channel”, the genus-2 manifold is built from gluing two three-punctured spheres, allowing us to access squares of OPE coefficients. In the “dumbbell channel”, the genus-2 partition function can be written as a sum of squared thermal one-point functions. I will explain convenient coordinate system for each channel. As an application, we focus on a simplifying limit of the genus-2 crossing equation, linking heavy-heavy-heavier OPE coefficients with thermal one-point coefficients in 3d CFTs.

Title: Using the OPE to look beyond horizons

Speaker: Nejc Čeplak

Based on: 2511.09638

Abstract: Black hole singularities leave distinct imprints on holographic correlation functions, traceable to bouncing geodesics: null geodesics that begin on one boundary of an eternal AdS black hole, reflect off the singularity, and reach a different boundary. Using the Operator Product Expansion (OPE), I will show that divergences in the complex-time plane of holographic correlation functions occur precisely at positions predicted by these geodesics, establishing a direct connection between the analytic structure of holographic correlators and black hole singularities. In this talk, I will discuss both neutral (Schwarzschild) and electrically charged black holes in AdS. In the latter case, I will show how the rich causal structure of the interior, including information about the inner horizon, is encoded in the analytic properties of holographic correlation functions.

Title: Thermal two-point functions and the black hole (not) interior

Speaker: Simon Caron-Huot

Based on: 2510.21673

Abstract: In AdS/CFT, fluctuations in some strongly coupled finite-temperature systems are related to Hawking radiation from a dual black hole. It is known that geodesics that approach the interior singularity imply specific correlations between rare, high-frequency Hawking quanta. I will explain how these leave various signatures in retarded and Wightman functions, in position, frequency and OPE space, for light and heavy fields, and can be calculated using bulk WKB geodesics. I will stress that the geodesics propagate inside a "copy" of the interior generated by analytic continuation of the exterior and have no obvious connections to the experience of an infalling observer.

Title: Bouncing off a stringy singularity

Speaker: Robin Karlsson

Based on: 2511.09616

Abstract: I will discuss boundary signatures of black hole geometries in holography. In particular, a sharp signature of the black hole singularity in holography is a divergence in the boundary thermal two-point function at a specific point in the complex time plane. This divergence arises from a null geodesic that bounces off the black hole singularity. At finite ’t Hooft coupling, stringy corrections to the bulk dynamics cannotbe neglected, and the fate of the bouncing geodesic is an open question. I will discuss how bouncing geodesics appear from QNMs and propose a simple scenario of how these singularities are smoothed out. This scenario resembles closely what happens in the SYK model. Based on 2511.09616 with Matthew Dodelson and Cristoforo Iossa.

Title: Temperature and conditions for thermalization after canonical quenches

Speaker: Lennart Dabelow

Based on: 2510.12696

Abstract: The long-time behavior of macroscopic systems is generically characterized by thermal equilibrium states. Yet it remains a fundamental challenge to explain this ubiquitous empirical fact from the quantum mechanical laws that govern individual atoms and molecules. Moreover, research into these foundations has also revealed a variety of phenomena where many-body quantum systems fail to thermalize, raising the question of general criteria for when thermal behavior can be expected. In this talk, we first introduce some context for how this challenge is addressed within the realm of nonrelativistic quantum mechanics. Thereafter, we specifically consider so-called quenches where a system is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. By means of a systematic expansion of the pre- and post-quench canonical ensembles in the quench strength, we obtain a prediction of the system's temperature after the quench as well as a hierarchy of necessary conditions for thermalization towards the (post-quench) canonical ensemble in the presence of additional conserved quantities. We illustrate the results numerically for a variety of setups involving integrable and nonintegrable models.

Title: "Filtering" CFTs at large N: Euclidean Wormholes, Closed Universes, and Black Hole Interiors

Speaker: Hong Liu

Based on: 2509.14327

Abstract: Despite its successes, the large-N holographic dictionary remains incomplete. Key features of gravitational path integrals--most notably Euclidean wormholes and the associated failure of factorization--lack a clear interpretation in the standard large-N framework. In this talk, we discuss a resolution of the puzzle by introducing a large-N filter, which provides an intrinsic boundary definition of gravitational "averages,'' and a boundary explanation of the origin of wormholes as well as their amplitudes. In addition, we derive an infinite tower of inequalities constraining wormhole amplitudes. Beyond resolving factorization, the large-N filter supplies a generalized framework from which richer Lorentzian spacetime structures can emerge, including closed universes and black hole interiors. We argue that both closed universes and black hole interiors are quantum volatile, and that an AdS spacetime entangled with a baby universe is likewise quantum volatile. This volatility may allow an observer in AdS to infer the existence of the baby universe, whereas for an infalling observer crossing a black hole horizon, the ability to make measurements after may become fundamentally limited--even if they may not live long enough to notice.

Title: The thermal bootstrap

Speaker: David Simmons-Duffin

Review talk

Title: Bootstrapping matrix quantum mechanics: equilibrium and nonequilibrium

Speaker: Minjae Cho

Based on: 2410.04262, 2508.04764, 2511.08560

Abstract: Large N matrix quantum mechanics provides an intriguing setup where fundamental questions about quantum gravity can be addressed in practice. In this talk, we discuss how a bootstrap framework based on imposing consistency conditions offers an efficient method to study its physics in both equilibrium and nonequilibrium settings. We first derive bootstrap bounds on its thermal equilibrium properties, which give access to black hole thermodynamics. We then introduce a heat sink for the matrix quanta through Lindblad dissipation dynamics, where the resulting bootstrap bounds provide strong evidence for the existence of a nonequilibrium phase transition.

Note: Due to technical issues, the video is not available. We would like to thank Minjae Cho for kindly making his slides available.

mqm boot eq noneq.pdf

Title: A Holographic prescription for generalized Schwinger-Keldysh contours

Speaker: Julio Virrueta

Based on: 2510.03404

Abstract: Large Real-time thermal correlators play an important role in our understanding of the holographic duality, relating thermal physics with black hole dynamics. In this context, the construction of a holographic dual to the Schwinger-Keldysh contour and its generalization is crucial. In this talk, I will present a new prescription for computing real-time thermal correlators with arbitrary operator ordering. The main idea is to construct a generalized Schwinger-Keldysh contour by gluing together different black hole geometries. After introducing this new bulk geometry, I will discuss how it can be used to evaluate higher-order thermal correlators in terms of contact Witten diagrams.

Title: Thermal field theory correlators in the large-N limit and the spectral duality relation

Speaker: Mile Vrbica

Based on: 2406.19790, 2505.14229, 2509.18074

Abstract: Correlation functions in thermal large-N theories (with a holographic dual) are expected to be meromorphic functions of the complex frequency. In this talk, I will discuss several analytic properties of retarded meromorphic correlators, relying heavily on their asymptotic properties and the thermal product formula. Immediate implications follow for the thermal spectra (QNMs) of theories related by double-trace deformations, where they can be shown to obey a “spectral duality relation”. I will present several examples where such a relation can be used to compute one spectrum from the other. Then I will turn to a more interesting case of the thermal CFT3 dual to the Einstein-Maxwell bulk. There, a set of dualities, similar to the particle-vortex self-duality, interplays interestingly with the so-called algebraically special structure of various bulk black hole solutions. This structure has a dramatic imprint on the boundary, where the spectral duality relation now imposes an infinite number of spectral constraints within the same theory.

Title: Towards a quantum lattice bootstrap

Speaker: Sean Hartnoll

Based on: 2509.18255, 2510.18950

Abstract: A “bootstrap” approach to physical systems starts from basic physical principles and aims to constrain the possible dynamics. The most successful instances, for the most part developed within high energy theory, have been the bootstrap of conformal field theories and the S-matrix bootstrap of relativistic field theories. I will explain how this methodology can be applied to condensed matter systems where the microscopic description is a lattice model. The basic ingredients are Lieb-Robinson type constraints combined with analyticity and positivity properties of Green’s functions. I will explain how one obtains bounds on transport coefficients and coupling constants from this approach.

Title: High to low temperature: O(N) model at large N

Speaker: Srijan Kumar

Based on: 2508.14872

Abstract: We study the O(N) vector model for scalars with quartic interaction at large N on S^1 x S^2 without the singlet constraint. The non-trivial fixed point of the model is described by a thermal mass satisfying the gap equation at large N. We obtain the partition function and the energy density for the model as a series at low temperature in units of the radius of the sphere. We show these results agree with the Borel-Padé extrapolations of the high temperature expansions of the partition function and energy density obtained in our previous work. This agreement validates both the expansions and demonstrates that low temperature expansions obtained here correspond to the same fixed point studied earlier at high temperature. We obtain the ratio of the partition function of the theory at the non-trivial fixed point to that of the Gaussian theory at all values of temperature. This ratio begins at 4/5 when the temperature is infinity, decreases to a minimum value of 0.760937, then increases and approaches unity as the temperature is decreased.

Title: The thermal representation of conformal ladder integrals

Speaker: Anastasios C. Petkou

Based on: 2508.16718

Abstract: I will present details of a recently discovered representation of conformal four-point ladder integrals as Thermal one-point functions in scalar field theories. Conformal ladder integrals can be constructed from the partition function of two harmonic oscillators twisted by an imaginary chemical potential. For any even dimension D and any loop order L they satisfy a familiar-looking second order differential equation. Thermal one-point functions of higher-spin operators correspond to linear combinations of multi-loop ladder graphs in D= 2 and D= 4 dimensions. A simple derivation for the all-loop resummation of conformal ladder integrals for arbitrary D is also given. Some possible connections if this work and recent developments in the thermal bootstrap, multiloop calculations, integrability, AdS/CFT and string theory will be discussed.

Title: Deep Finite Temperature Bootstrap

Speaker: Vasilis Niarchos

Based on: 2508.08560

Abstract: I will discuss a new way to bootstrap crossing equations in CFT that relies on the use of dispersion relations and efficient ways to optimize over spaces of functions. In this approach, one does not only bootstrap specific CFT data, but also full tails of OPE expansions, reconstructing approximate crossing-symmetric correlation functions. As a concrete demonstration, I will present how the method works in the context of the thermal bootstrap, highlighting the differences from previous approaches, comparative advantages and potential pitfalls and difficulties that can arise.

Title: Holographic Correlators from Thermal Bootstrap

Speaker: Ilija Burić

Based on: 2508.08373

Abstract: The thermal bootstrap, a method based on the partial wave decomposition and Euclidean-time periodicity (KMS invariance) of finite-temperature two-point functions, has recently led to various results in the critical Ising and O(N) models. In this talk, we apply the thermal bootstrap to holographic CFTs. Starting from the well-understood thermal coefficients of the stress tensor and its composites, we use the KMS sum rules and Pade-Borel resummation techniques to obtain thermal coefficients of double-trace operators. The result passes several checks, including a comparison with solutions to the Klein-Gordon equation on the planar AdS black hole. The talk is based on the joint work with Ivan Gusev and Andrei Parnachev, 2508.08373.

Title: EFTs for thermal dynamics in QFT

Speaker: Luca Delacrétaz

Based on: 2505.06869 and 2310.10564

Abstract: After a brief review of how thermal effective actions capture equilibrium physics in QFT, I will turn to dynamics and describe the Schwinger-Keldysh EFTs that control the near-equilibrium, real time, behavior. I will describe precision tests of these EFTs in lattice models that are simpler to simulate. I will show how one can identify a strong coupling scale in these EFTs, which bounds how fast a system can thermalize and let hydrodynamics emerge. For generic QFTs and CFTs, this establishes the Planckian bound on their thermalization time, tau_{eq}> hbar / T. If time permits, I may discuss the special case of 1+1d QFTs, where low dimensionality allows for additional control on the thermalization dynamics.

Title: Out-of-bounds hydrodynamics in holographic anisotropic Dirac semimetals

Speaker: Ignacio Salazar Landea

Based on: 2507.13497

Abstract: We present a version of a strongly correlated 2+1-dimensional condensed matter system that features a phase transition between a semimetal and an insulator through a semi-Dirac quantum critical region using AdS/CFT. Our construction relies on deforming a relativistic UV fixed point with some relevant operators that explicitly break rotations and some internal symmetries. We probe this construction by computing fermionic dispersion relations and the shear viscosity. We find a new instance of parametric violation of the KSS-bound with the \eta/s ratio featuring a monotone dependence on temperature fixed by a Lifshitz dynamical critical exponent. Finally, we check this anisotropic scaling by constructing explicit T=0 solutions.

Title: Classical spin liquids from frustrated Ising models in hyperbolic space

Speaker: Johanna Erdmenger

Based on: 2506.02113

Abstract: The `discrete holography’ programme aims at establishing a holographic duality for discrete systems. For instance, when reducing to a regular tiling of hyperbolic space, the action of JT gravity reduces to an Ising model on this space with particular boundary conditions. Moreover, discrete hyperbolic systems are also of great interest for condensed matter physics. In view of both motivations, I will present recent results on hyperbolic frustrated Ising models at finite temperature. The shape of the boundary may be used to control low-energy states: Depending on the boundary, ordered or disordered ground states are found. These results demonstrate how geometric frustration acts in curved space to produce classical spin liquids.

Title: Quantum critical dynamics of the Ising model in 2 spatial dimensions

Speaker: Subir Sachdev

Review talk

Abstract: I will consider the simplest models of quantum critical points without quasiparticle excitations: the Ising model and the Bose Hubbard model in 2+1 dimensions. The traditional methods of quantum criticality, epsilon or large N expansion or bootstrap, fail in providing a controlled description of their real-time Planckian dynamics. I will discuss how the dynamics has been addressed using semi-classical and holographic methods.

Title: The quantum Mpemba effects

Speaker: Sara Murciano

Based on: 2502.08087

Abstract: The Mpemba effect, where a hotter system can equilibrate faster than a cooler one, has long been a subject of fascination in classical physics. In this talk, I will focus on a quantum version of this phenomenon in extended many-body systems in which a symmetry is explicitly broken by the initial state, but it is restored by the time evolution. To study this phenomenon we introduce a new quantity, dubbed entanglement asymmetry, which is a measure of symmetry breaking inspired by the theory of entanglement in many-body states. Beyond the theoretical framework, I will present experimental observations and the fundamental mechanisms that give rise to anomalous relaxation behaviors, especially on the role of quantum fluctuations and integrability.

Title: Extracting 3D CFT Data from Thermal Correlators

Speaker: Francesco Mangialardi

Based on: 2506.21671

Abstract: I will describe how correlation functions of a conformal field theory placed on the thermal geometry S^1 x S^2 can be used to obtain precise information about flat space CFT data, namely the spectrum and the OPE coefficients of primary operators. The focus will be primarily on thermal one-point functions. Although exact formulas for thermal one-point blocks are not known in this setting, I will explain how the Casimir equation they satisfy provides enough control to obtain series expansions of blocks in different regimes of their parameter space, as well as to derive an inversion formula that expresses OPE coefficients in terms of thermal one-point functions. These tools enable us to extract information about OPE coefficients across the entire spectrum of exchanged operators, combining exact data for low-lying operators with systematic asymptotic expansions in the heavy exchange regime. I will illustrate these results using the free theory as an example.

Title: An Analytic Bootstrap Framework for Thermal CFTs

Speaker: Deniz Bozkurt

Based on: 2506.06422

Abstract: I will present new universal formulae for thermal two-point functions of scalar operators in conformal field theories, derived using dispersion relations. In complex τ plane, this approach captures the analytic structure of thermal correlators and satisfies all thermal bootstrap conditions, up to theory-specific dynamical input. At non-zero spatial separation, we extend the construction via method of images, yielding a correlator consistent with KMS condition and thermal OPE behavior. While clustering at infinite distance must be checked case-by-case, we verify our framework across a range of theories, including perturbative theories and strongly-coupled models. Notably, we improve the asymptotics of heavy states estimated by Tauberian theorems and we produce novel results for the 3d Ising model in agreement with Monte Carlo simulations. This work builds toward a analytic bootstrap framework for thermal CFTs, bridging insights from both weak and strong coupling regimes.

Title: OPE and Thermal Holography

Speaker: Andrei Parnachev

Based on: 2505.10277

Abstract: Thermal two-point functions in holographic CFTs receive contributions from two parts. One part comes from the identity, the stress tensor and multi-stress tensors and constitutes the stress-tensor sector. The other part consists of contribu- tions from double-trace operators. The sum of these two parts must satisfy the KMS condition – it has to be periodic in Euclidean time. The stress-tensor sector can be computed by analyzing the bulk equations of motions near the AdS boundary and is not periodic by itself. We show that starting from the expression for the stress-tensor sector one can impose the KMS condition to fix the double-trace part, and hence the whole correlator. We perform explicit calculations in the asymptotic approximation, where the stress-tensor sector can be computed exactly. One can either sum over the thermal images of the stress-tensor sector and subtract the singularities or solve for the KMS condition directly and perform the Borel resummation of the resulting double-trace data – the results are the same.

Title: Thermal EFT and Universality of Rényi entropy in CFT

Speaker: Sridip Pal

Based on: 2503.24353

Abstract: I will introduce the thermal effective field theory (EFT), which captures the high-temperature expansion of the partition function of a CFT. The thermal EFT comes with a set of Wilson coefficients. We will show that the same set of Wilson coefficients controls the behavior of the density of states for large eigenvalues of the modular Hamiltonian, coming from the vacuum of a CFT, reduced on a spherical region. More concretely, we use the thermal EFT to prove that, for the vacuum state in any conformal field theory in d dimensions, the n-th Rényi entropy S_A^(n) behaves as S_A^(n) = f/(2\pi n)^{d-1} ((Area(\partial A))/(d-2)\epsilon^{d-2}) (1+O(n)) in the n --> 0 limit when the boundary of the entanglement domain A is spherical with the UV cutoff \epsilon. The theory dependence is encapsulated in the cosmological constant f in the thermal effective action. Using this result, we estimate the density of states for large eigenvalues of the modular Hamiltonian for the domain A.

Title: Thermal effective actions from conformal boundary conditions in gravity

Speaker: Batoul Banihashemi

Based on: 2503.17471

Abstract: We study thermodynamics of gravitational systems with conformal boundary conditions, where the conformal class of the boundary metric and the trace of the extrinsic curvature K are held fixed. In the high temperature limit the series of subextensive terms in the free energy are compared to predictions from thermal effective field theory. In all considered cases there is agreement in the structure of the high temperature expansion. Interestingly, the first subextensive correction to the free energy is negative, violating a conjectured bound on this coefficient in quantum field theory. We interpret this as a signal that gravity does not fully decouple in the putative boundary dual. Ensembles with negative K are tied to solutions with cosmic-type horizons, where the system boundary is smaller than the horizon. In some cases, these solutions dominate the phase diagram and are necessary for consistency with thermal effective field theory.

Title: Thermal Product Formula for Shear Modes

Speaker: Jyotirmoy Bhattacharya

Based on: 2504.17781

Abstract: In this talk, I will begin by reviewing previous work on a product formula that expresses holographic thermal two-point functions in terms of the quasi-normal modes of the dual black brane. I will then discuss a generalization of this formula for two-point functions of conserved currents whose components mix non-trivially. In particular, I will focus on shear channel fluctuations of R-charged black branes in five-dimensional AdS, where the shear mode couples to the charge diffusion mode at non-zero momentum. A key step in deriving the generalized formula is the decoupling of the corresponding bulk equations. I will also present a similar formula for the case involving a boundary global R-symmetry anomaly, when a bulk Chern-Simons term is present, and it introduces additional couplings in the shear channel. In addition, drawing on insights from the quasi-normal mode spectrum, I will report about an instability, as well as the presence of high-momentum, long-lived modes associated with large values of the anomaly coefficient. I will conclude with an outlook and some speculations on the future implications of these results.

Title: Subsystem entropy in 2d CFT and the diagonal approximation

Speaker: Anatoly Dymarsky

Based on: 2409.19046, 2409.19271

Abstract: Entanglement entropy is a key quantity in quantum many-body physics, yet its computation remains challenging outside of special cases. In this talk, I will present a method based on the diagonal approximation, rooted in the subsystem Eigenstate Thermalization Hypothesis (ETH), for evaluating the entanglement entropy of excited states and thermal ensembles in the large-subsystem limit. Applying this framework to two-dimensional conformal field theories (2D CFTs), we show that it reproduces known results for canonical and microcanonical ensembles and individual primary states, while also yielding new predictions for KdV generalized Gibbs ensembles. Our approach resolves tensions between explicit CFT computations and ETH expectations, providing indirect support for the generalized ETH in 2D CFTs.

Title: Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime

Speaker: Waltraut Knop

Based on: 2502.01734

Abstract: In this talk, I will explore thermal two-point functions and specific classes of four-point functions in generic symmetric product orbifold CFTs. Remarkably, these correlators exhibit universality: they are independent of the details of the seed theory, only depending on the orbifold structure. At large N, these universal correlators match semiclassical correlation functions of fields on an AdS3 black hole background. This is particularly surprising given that these CFTs are not dual to semiclassical gravity. I will further connect these findings to recent conjectures involving von Neumann algebra techniques, highlighting that the proposed conditions on thermal two-point functions are insufficient to diagnose the presence of horizons.

Title: High temperature behaviour of confining Lattice Gauge Theories

Speaker: Michele Caselle

Based on: 2407.10678 , 2501.16185

Abstract: Lattice Gauge Theories (LGTs) undergo a deconfinement transitions as the temperature increases. An interesting feature of LGTS is that at high temperature, but still in the confining phase (i.e. approaching the deconfinement transition from below), several simplifications occur and the non-perturbative behaviour of the theory can be described using effective models and in particular the so called "Effective String Theory" (EST). In this talk, after a brief introduction to LGTs and EST, I will discuss a few relevant predictions of these models and compare them with the results of Monte Carlo simulation. In particular, if time allows, I will discuss:

-The temperature dependence of the interquark potential

-The interpretation of the deconfinement transition as a Hagedorn transition of the EST.

Title: The large N vector model on a sphere and at finite temperature

Speaker: Justin Raj David

Based on: 2212.07758, 2307.14847, 2406.14490, 2411.18509

Abstract: The O(N) vector model with a quartic interaction in 3 dimensions is one of the most well studied quantum field theories. It is important to describe strongly correlated physics and its non-trivial fixed point at large N serves as the holographic dual to Vasiliev's higher spin theory on AdS_3. In spite of the extensive studies, there is no systematic study of the model on S^1\times S^2. We develop a method to evaluate the partition function and energy density of a massive scalar on a 2-sphere of radius r and at finite temperature beta as power series in beta/r. Each term in the power series can be written in terms of polylogarithms. We use this result to obtain the gap equation for the large N, critical O(N) in the large radius expansion. Solving the gap equation perturbatively we obtain the leading finite size corrections to thermal one-point functions in the model. This includes one-point functions of the higher spin, s>2 currents of the model for which we use the Euclidean inversion formula. The talk will begin with a brief introduction to the relevance of finite temperature physics in holography.

Title: Lessons from a microscopic derivation of dissipative terms in Schwinger-Keldysh effective field theories

Speaker: Giorgio Frangi

Based on: 2501.16441

Abstract: The recent development of a procedure to derive effective actions to describe dissipative hydrodynamics, based on the closed time path formalism of QFT, proved to be key in shedding light on many interesting and diverse phenomena. In this talk, I will discuss how dissipative terms in these EFTs arise from explicitly performing a Wilsonian renormalisation procedure, thus giving them a microscopic foundation that has so far been elusive. I will show how these terms can be precisely traced back to a specific type of singularity typical of thermal field theories, thus elucidating the relationship between this novel EFT approach and earlier studies on IR properties of thermal correlators as calculated from microscopic theories. I will then outline how this procedure naturally leads to the definition of an enhanced space of couplings, where novel types of RG fixed point may be located, and conclude by providing one such example.

Title: Ringdown at finite coupling

Speaker: Matthew Dodelson

Based on: 2501.06170, 2408.05790

Abstract: Thermal correlators in large N systems equilibrate at late times, but the precise late-time behavior is unknown away from holographic and free field limits. In this talk I will analyze this problem in the case of the SYK model away from the low-temperature limit. I will then explain how to think about the result in terms of a black hole.

Title: Soft mode action for the large-p SYK model

Speaker: Marta Bucca

Based on: 2412.14799

Abstract: The physics of the SYK model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In previous works, the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schwarzian. Here, we will give two alternative derivations of the full nonlinear effective action in the large p limit, where p is the number of fermions in the interaction terms of the Hamiltonian. We will then generalise our results for the large-p SYK chain and obtain a "Schwarzian chain" effective action for it. This will allow us to study the SYK chain in the hydrodynamic limit.

Title: Thermal Correlators and Black Hole Singularities

Speaker: Samuel Valach

Based on: 2404.17286

Abstract: Black hole singularities in AdS are reflected in the so-called bouncing geodesics. In the dual CFT, these are manifested as "bouncing singularities" in the thermal correlator. I will explain both sides of this problem and demonstrate how these singularities arise from the analytic properties of the stress-tensor sector of the boundary CFT.

Title: Temperature-Resistant Order in 2+1 Dimensions

Speaker: Fedor K. Popov (Федор Попов)

Based on: 2412.09459

Abstract: High temperatures are typically thought to increase disorder. Here we examine this idea in Quantum Field Theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking Z2→∅ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with non-local interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields.

Title: From the Cubic CFT to the Quantum Loop model

Speaker: Junchen Rong

Based on: 2205.04472, 2309.05715, 2412.01503

Abstract: I will present how recent advancements in the bootstrap analysis of the O(3) conformal field theory (CFT) have led to the prediction of a novel phase in the fully packed quantum loop model on the triangular lattice. This theoretical prediction has been confirmed by quantum Monte Carlo simulations. Furthermore, I will delve into the challenges involved in unraveling the finite-temperature phase transition emerging from this phase. The talk is based on Arxiv:2205.04472, 2309.05715 and 2412.01503.

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