Two-dimensional conformal field theory and the butterfly effect

TL;DR

This paper investigates chaos in two-dimensional conformal field theories by analyzing out-of-time order correlators, revealing exponential decay after a delay related to the scrambling time and operator energies, using large central charge Virasoro blocks.

Contribution

It demonstrates how to compute out-of-time order correlators in 2D CFTs via Virasoro blocks, connecting bulk calculations with boundary chaos diagnostics.

Findings

Correlators decay exponentially after a delay proportional to the scrambling time.

The decay onset depends logarithmically on the central charge and operator energies.

Bulk calculations align with boundary chaos behavior in 2D CFTs.

Abstract

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time order thermal correlators of the form $\langle W(t)VW(t)V\rangle$. We reproduce bulk calculations similar to those of [1], by studying the large $c$ Virasoro identity block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of $\sim t_* - \frac{\beta}{2\pi}\log \beta^2E_w E_v$, where $t_*$ is the scrambling time $\frac{\beta}{2\pi}\log c$, and $E_w,E_v$ are the energy scales of the $W,V$ operators.