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 ω* = iλ 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 λ in c > 1 compact, unitary CFT2s identical to the chaos bound, λ ≤ 2πT. This bound is saturated in large c CFT2s with a sparse light spectrum, as quantified by [1], for all temperatures above the dual Hawking-Page transition temperature.
Highlights
JHEP12(2021)006 to an upper bound on λL, λL ≤ 2βπ, with the bound saturated in holographic systems with black holes present in the bulk [7]
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 ω∗ = iλ 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
Summary
We review some salient features of holographic conformal field theories that will be relevant for our analysis. We sketch the gravitational arguments for pole skipping in holographic response functions, where the peculiar non-analyticities emerge as a consequence of the near-horizon geometry in black hole backgrounds. We turn to two-dimensional conformal field theories and review the constraints imposed on the spectrum by bulk thermodynamic considerations
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