Thermal Seminars - Recordings

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

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 Popov

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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