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Comments on Thermalization in 2D CFT

Jan de Boer, Dalit Engelhardt

TL;DR

The work analyzes thermalization in 2D CFTs, distinguishing rational and non-rational spectra and distinguishing local from global thermalization. It uses boundary-state constructions and holographic duals to show that global thermalization is unlikely in generic diffeomorphisms of the ground state, while local thermal behavior can emerge; the generalized Gibbs ensemble maps to a BTZ-like bulk with boundary deformations, implying limited impact of extra charges at large $c$. The paper also connects periodicity in correlation functions to the rationality of the spectrum and discusses the holographic interpretation via Chern–Simons gravity and the KdV hierarchy. Overall, it argues that at large $c$ the extra conserved charges do not qualitatively alter the BTZ-dominated thermalization picture and outlines several avenues for future exploration, including AdS/BCFT extensions and quantum hair considerations.

Abstract

We revisit certain aspects of thermalization in 2D CFT. In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a BTZ black hole. The extra conserved charges, while rendering $c < 1$ theories essentially integrable, therefore seem to have little effect on large-$c$ conformal field theories.

Comments on Thermalization in 2D CFT

TL;DR

The work analyzes thermalization in 2D CFTs, distinguishing rational and non-rational spectra and distinguishing local from global thermalization. It uses boundary-state constructions and holographic duals to show that global thermalization is unlikely in generic diffeomorphisms of the ground state, while local thermal behavior can emerge; the generalized Gibbs ensemble maps to a BTZ-like bulk with boundary deformations, implying limited impact of extra charges at large . The paper also connects periodicity in correlation functions to the rationality of the spectrum and discusses the holographic interpretation via Chern–Simons gravity and the KdV hierarchy. Overall, it argues that at large the extra conserved charges do not qualitatively alter the BTZ-dominated thermalization picture and outlines several avenues for future exploration, including AdS/BCFT extensions and quantum hair considerations.

Abstract

We revisit certain aspects of thermalization in 2D CFT. In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a BTZ black hole. The extra conserved charges, while rendering theories essentially integrable, therefore seem to have little effect on large- conformal field theories.

Paper Structure

This paper contains 9 sections, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Probes of local and global thermalization
  3. Non-equilibrium behavior from CFT boundary states
  4. Revivals in finite-length systems
  5. Operator spectrum dependence of thermalization
  6. General setup
  7. Periodicity in correlation functions
  8. The holographic dual of the generalized Gibbs ensemble
  9. Discussion

Figures (2)

  • Figure 1: The Schwarz-Christoffel conformal transformation that maps the UHP with designated prevertices to a rectangle.
  • Figure 2: Periodicity in observables in the rectangle ground state. Plot parameters are $k=0.5$ and $L=1$.