Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.22679

On the temperature dependence of quasinormal modes in SYK and holography

Matthew Dodelson, Om Gupta, Márk Mezei, Diandian Wang

Published Jun 21, 2026• 0 citations
arXivHTMLPDF

Abstract

It was recently found that the quasinormal modes (or Ruelle--Pollicott resonances) of the SYK model at infinite temperature form a Christmas tree shape, reminiscent of AdS black holes. We generalise this computation to finite temperature, allowing us to continuously connect the infinite temperature results to the low temperature regime dual to JT gravity. We contrast the movement of the quasinormal modes with a few examples: various AdS black holes, dynamical phase transitions, and the large $p$ SYK chain. We find that the relaxation rate increases monotonically with temperature only at strong coupling, corresponding to the gravitational regime. Byproducts of our investigations are new results on operator growth that may be of independent interest.

DOI
10.48550/arxiv.2606.22679

Related papers

Ringdown in the SYK model

Matthew Dodelson

We analyze thermal correlators in the Sachdev-Ye-Kitaev model away from the maximally chaotic limit. Despite the absence of a weakly curved black hole dual, the two point function decomposes into a sum over a discrete set of quasinormal modes. To compute the spectrum of modes, we analytically solve the Schwinger-Dyson equations to a high order in perturbation theory, and then numerically fit to a sum of exponentials using a technique analogous to the double cone construction. The resulting spectrum has a tree-like structure which is reminiscent of AdS black holes with curvature singularities. We present a simple toy model of stringy black holes that qualitatively reproduces some aspects of this structure.

arXiv:2408.05790•SciPost Physics•Sep 30, 2025•6 citations

The coupled SYK model at finite temperature

Xiao-Liang Qi, Pengfei Zhang

Abstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.

arXiv:2003.03916•Journal of High Energy Physics•May 26, 2020•27 citations

Black-Hole Signatures in the Finite-Temperature Critical Ising Chain

Zuo Wang, Liang He

We demonstrate that the finite-temperature critical transverse-field Ising chain exhibits quantitative signatures of black-hole physics in its dual gravitational description within the AdS/CFT correspondence. Its finite-temperature dynamics and thermodynamics are consistently captured by a mixed thermal-AdS/BTZ black hole saddle, leading to three mutually compatible observations. First, antipodal excitation transport collapses onto a universal temperature-dependent curve determined by the relative AdS and BTZ contributions to the gravitational partition function, reflecting horizon absorption. Second, in the high-temperature regime, the retarded response exhibits exponential relaxation governed by the lowest quasi-normal mode of the dual black hole. Third, the temperature derivative of the von Neumann entropy develops a pronounced minimum at a temperature consistent with the Hawking-Page transition. These results identify critical quantum spin chains as minimal and experimentally accessible platforms for probing dynamical and thermodynamic aspects of quantum black holes in controllable many-body systems.

quant-pharXiv:2603.07639•Mar 10, 2026•0 citations

The coupled SYK model at finite temperature

Xiao-Liang Qi

Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.

•Jul 4, 2023•33 citations

Large N Fields and Holography

Animik Ghosh

We study (nearly) AdS/CFT holography within the context of the Sachdev-Ye- Kitaev (SYK) model. We present a systematic procedure to extract the dynamics of the low energy Schwarzian mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the infrared within the framework of perturbation theory. We develop a systematic approach using Feynman diagrams in bilocal theory to obtain a formal expression for the enhanced and O(1) corrections to the bilocal propagator and apply this general technique to large q SYK. We show that the Schwarzian theory describes a sector of a general class of two dimensional CFTs using conformal bootstrap techniques. We also provide a gravitational interpretation of this fact by showing that the dynamics in the near horizon throat of a specific class of BTZ black holes is described very well by Jackiw-Teitelboim (JT) gravity which gives rise to the Schwarzian action. We study the highly nontrivial conformal matter spectrum of the SYK model at arbitrary q. We provide a three dimensional bulk interpretation and carry out Kaluza-Klein (KK) reduction to reproduce the SYK spectrum and more significantly, the conformal bilocal propagator. We provide an interpretation of the two dimensional dual spacetime of the conformal sector of the SYK model using techniques from bilocal holography. We present a resolution of a conundrum about the signature of the dual spacetime using nonlocal integral transformations.

•Aug 4, 2020•0 citations

Relaxation in conformal field theory, Hawking-Page transition, and quasinormal or normal modes

Danny Birmingham, Ivo Sachs, Sergey N. Solodukhin

We study the process of relaxation back to thermal equilibrium in $(1+1)$-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with the characteristic period set by the size of the system. We then analyze the intermediate regime in two specific models: namely, free fermions, and a strongly coupled large k conformal field theory which is dual to string theory on $(2+1)$-dimensional anti--de Sitter spacetime. In the latter case, there is a sharp transition between the two regimes in the $k=\ensuremath{\infty}$ limit, which is a manifestation of the gravitational Hawking-Page phase transition. In particular, we establish a direct connection between quasinormal and normal modes of the gravity system, and the decaying and oscillating behavior of the conformal field theory.

arXiv:hep-th/0212308•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 30, 2003•90 citations
It was recently found that the quasinormal modes (or Ruelle--Pollicott resonances) of the SYK model at infinite temperature form a Christmas tree shape, reminiscent of AdS black holes. We generalise this computation to finite temperature, allowing us to continuously connect the infinite temperature results to the low temperature regime dual to JT gravity. We contrast the movement of the quasinormal modes with a few examples: various AdS black holes, dynamical phase transitions, and the large ppp SYK chain. We find that the relaxation rate increases monotonically with temperature only at strong coupling, corresponding to the gravitational regime. Byproducts of our investigations are new results on operator growth that may be of independent interest.
We analyze thermal correlators in the Sachdev-Ye-Kitaev model away from the maximally chaotic limit. Despite the absence of a weakly curved black hole dual, the two point function decomposes into a sum over a discrete set of quasinormal modes. To compute the spectrum of modes, we analytically solve the Schwinger-Dyson equations to a high order in perturbation theory, and then numerically fit to a sum of exponentials using a technique analogous to the double cone construction. The resulting spectrum has a tree-like structure which is reminiscent of AdS black holes with curvature singularities. We present a simple toy model of stringy black holes that qualitatively reproduces some aspects of this structure.
Abstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.
We demonstrate that the finite-temperature critical transverse-field Ising chain exhibits quantitative signatures of black-hole physics in its dual gravitational description within the AdS/CFT correspondence. Its finite-temperature dynamics and thermodynamics are consistently captured by a mixed thermal-AdS/BTZ black hole saddle, leading to three mutually compatible observations. First, antipodal excitation transport collapses onto a universal temperature-dependent curve determined by the relative AdS and BTZ contributions to the gravitational partition function, reflecting horizon absorption. Second, in the high-temperature regime, the retarded response exhibits exponential relaxation governed by the lowest quasi-normal mode of the dual black hole. Third, the temperature derivative of the von Neumann entropy develops a pronounced minimum at a temperature consistent with the Hawking-Page transition. These results identify critical quantum spin chains as minimal and experimentally accessible platforms for probing dynamical and thermodynamic aspects of quantum black holes in controllable many-body systems.
Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.
We study (nearly) AdS/CFT holography within the context of the Sachdev-Ye- Kitaev (SYK) model. We present a systematic procedure to extract the dynamics of the low energy Schwarzian mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the infrared within the framework of perturbation theory. We develop a systematic approach using Feynman diagrams in bilocal theory to obtain a formal expression for the enhanced and O(1) corrections to the bilocal propagator and apply this general technique to large q SYK. We show that the Schwarzian theory describes a sector of a general class of two dimensional CFTs using conformal bootstrap techniques. We also provide a gravitational interpretation of this fact by showing that the dynamics in the near horizon throat of a specific class of BTZ black holes is described very well by Jackiw-Teitelboim (JT) gravity which gives rise to the Schwarzian action. We study the highly nontrivial conformal matter spectrum of the SYK model at arbitrary q. We provide a three dimensional bulk interpretation and carry out Kaluza-Klein (KK) reduction to reproduce the SYK spectrum and more significantly, the conformal bilocal propagator. We provide an interpretation of the two dimensional dual spacetime of the conformal sector of the SYK model using techniques from bilocal holography. We present a resolution of a conundrum about the signature of the dual spacetime using nonlocal integral transformations.
We study the process of relaxation back to thermal equilibrium in (1+1)(1+1)(1+1)-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with the characteristic period set by the size of the system. We then analyze the intermediate regime in two specific models: namely, free fermions, and a strongly coupled large k conformal field theory which is dual to string theory on (2+1)(2+1)(2+1)-dimensional anti--de Sitter spacetime. In the latter case, there is a sharp transition between the two regimes in the $k=\ensuremath{\infty}$ limit, which is a manifestation of the gravitational Hawking-Page phase transition. In particular, we establish a direct connection between quasinormal and normal modes of the gravity system, and the decaying and oscillating behavior of the conformal field theory.