Relaxation in Conformal Field Theory, Hawking-Page Transition, and Quasinormal/Normal Modes

TL;DR

This paper investigates how conformal field theories relax to thermal equilibrium, revealing a transition from exponential decay to oscillatory behavior, and links these dynamics to gravitational quasinormal and normal modes across different regimes.

Contribution

It provides a detailed analysis of relaxation dynamics in 1+1D conformal field theories, connecting field theory behavior with gravitational quasinormal and normal modes, especially highlighting the Hawking-Page transition.

Findings

Exponential decay of perturbations in large systems

Oscillatory relaxation in small inverse temperature regimes

Connection between quasinormal modes and relaxation behavior

Abstract

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 characteristic period set by the size of the system. We then analyse the intermediate regime in two specific models, namely free fermions, and a strongly coupled large $\tt k$ 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 ${\tt k}=\infty$ 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 behaviour of the conformal field theory.