Chaos and pole skipping in CFT$_2$

TL;DR

This paper explores the connection between quantum chaos and pole skipping in 2D conformal field theories on a torus, revealing how pole skipping relates to the central charge, stress tensor, and chaos bound, especially in large c theories.

Contribution

It demonstrates how pole skipping locations are determined by CFT parameters and establishes a chaos bound in 2D CFTs, saturating in large c theories with sparse spectra.

Findings

Pole skipping location depends on central charge and stress tensor expectation.

Chaos bound $ ext{Im}( ext{frequency}) \, \leq 2\pi T$ is confirmed in these theories.

Large c theories with sparse spectra saturate the chaos bound.

Abstract

Recent work has suggested an intriguing relation between quantum chaos and energy density correlations, known as pole skipping. We investigate this relationship in two dimensional conformal field theories on a finite size spatial circle by studying the thermal energy density retarded two-point function on a torus. We find that the location $\omega_* = i \lambda$ of pole skipping in the complex frequency plane is determined by the central charge and the stress energy one-point function $\langle T\rangle$ on the torus. In addition, we find a bound on $\lambda$ in $c>1$ compact, unitary CFT$_2$s identical to the chaos bound, $\lambda \leq 2\pi T$. This bound is saturated in large $c$ CFT$_2$s with a sparse light spectrum, as quantified by arXiv:1405.5137, for all temperatures above the dual Hawking-Page transition temperature.