Out-of-time-ordered correlators and purity in rational conformal field theories

Abstract

In this paper we investigate measures of chaos and entanglement in rational conformal field theories in 1 + 1 dimensions. First, we derive a 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 SS -matrix elements known as anyon monodromy scalar. Next, in the explicit setup of an SU(N)kSU(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- cc limit, the purity grows logarithmically as in holographic theories; in contrast, the out-of-time-ordered correlators remain, in general, nonvanishing.