Comments on Thermalization in 2D CFT

TL;DR

This paper examines thermalization processes in 2D conformal field theories, highlighting differences between rational and non-rational cases, and discusses the holographic duals of generalized Gibbs ensembles.

Contribution

It provides a detailed analysis of thermalization in 2D CFTs, including the construction of holographic duals for generalized Gibbs ensembles and insights into their thermalization behavior.

Findings

States obtained by diffeomorphisms can appear locally thermal.

Time-dependent energy-momentum tensor is a poor global thermalization diagnostic.

Large-c theories are minimally affected by conserved charges in the holographic dual.

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.