Chaos and pole skipping in CFT${}_2$

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 ${\omega }_{\ast }=i\lambda$ of pole skipping in the complex frequency plane is determined by the central charge and the stress energy one-point function $⟨T⟩$ on the torus. In addition, we find a bound on $\lambda$ in $c>1$ compact, unitary CFT${}_2$s identical to the chaos bound, $\lambda \le 2\pi T$. 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.

16 pages, 2 figures

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• Subleading Bounds on Chaos
• Construction of bulk solutions for towers of pole-skipping points
• Extremal Chaos
• Scrambling with conservation law
• Quantum information scrambling and quantum chaos in little string theory