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

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 $ensuremath{sim}{t}_{*}ensuremath{-}(ensuremath{beta}/2ensuremath{pi})mathrm{log}{ensuremath{beta}}^{2}{E}_{w}{E}_{v}$, where ${t}_{*}$ is the fast scrambling time $(ensuremath{beta}/2ensuremath{pi})mathrm{log}c$ and ${E}_{w},{E}_{v}$ are the energy scales of the $W,V$ operators.