Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory

Abstract

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time-order thermal correlators of the form ⟨W(t)VW(t)V⟩. We reproduce holographic calculations similar to those of Shenker and Stanford, by studying the large c Virasoro identity conformal block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of ~t[subscript *] - (β/2π)logβ[superscript 2]E[subscript w]E[subscript v], where t[subscript *] is the fast scrambling time (β/2π)logc and E[subscript w],E[subscript v] are the energy scales of the W,V operators.