Conformal field theory and the web of quantum chaos diagnostics

TL;DR

This paper explores three chaos diagnostics in 2D conformal field theories, revealing their interconnections through analytic continuations of the torus partition function and examining the transition from rational to irrational theories.

Contribution

It uncovers how spectral form factor, out-of-time-ordered correlators, and operator entanglement relate via analytic continuations, and analyzes the emergence of chaos in CFTs.

Findings

All three chaos diagnostics derive from the torus partition function.

Rational CFTs exhibit emergent irrationality in large-N limits.

The breakdown of rationality correlates with increased chaos in theories.

Abstract

We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that all three quantities may be obtained by different analytic continuations of the torus partition function, we address the connections and distinctions between the information that each quantity provides us. In this process, we study the emergence of irrationality from "large-N" limits of rational conformal field theories (RCFTs) as well as the explicit breakdown of rationality for theories with central charges greater than the number of their conserved currents. Our analysis begins to elucidate the intermediate dynamical behavior of theories that bridge the gap between integrable RCFTs and maximally chaotic holographic CFTs.