Scrambling without chaos in RCFT

TL;DR

This paper derives a universal formula for chaos measures in rational conformal field theories, revealing distinct late-time behaviors of correlators and entanglement, with implications for understanding quantum chaos.

Contribution

It provides the first universal late-time formula for out-of-time-ordered correlators in RCFTs, connecting chaos measures to modular S-matrix elements.

Findings

Universal late-time out-of-time-ordered correlator formula derived

Purity grows logarithmically in large-c limit, similar to holographic theories

Out-of-time-ordered correlators remain non-vanishing at late times

Abstract

In this paper we investigate measures of chaos and entanglement in rational conformal field theories in 1+1 dimensions. First, we derive a universal formula for the late time value of the out-of-time-ordered correlators for this class of theories. Our universal result can be expressed as a particular combination of the modular S-matrix elements known as the anyon monodromy scalar. Next, in the explicit setup of a $SU(N)_k$ Wess-Zumino-Witten model, we compare the late time behavior of the out-of-time-ordered correlators and the purity. Interestingly, in the large-c limit, the purity grows logarithmically as in holographic theories; in contrast, the out-of-time-ordered correlators remain, in general, non-vanishing.