A Quantum Correction To Chaos

TL;DR

This paper investigates quantum corrections to chaos in two-dimensional conformal field theories at large central charge, revealing how $1/c$ effects modify the Lyapunov exponent and discussing implications for chaos bounds and bulk locality.

Contribution

It provides a detailed analysis of $1/c$ corrections to chaos diagnostics in CFT$_2$, clarifying their impact on the Lyapunov exponent and the chaos bound.

Findings

Lyapunov exponent receives $1/c$ corrections, modifying the chaos rate.

Out of time order correlators have additional $1/c$ suppressed contributions.

Results do not conflict with the chaos bound due to these corrections.

Abstract

We use results on Virasoro conformal blocks to study chaotic dynamics in CFT$_2$ at large central charge c. The Lyapunov exponent $\lambda_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be interpreted as $\lambda_L = \frac{2 \pi}{\beta} \left( 1 + \frac{12}{c} \right)$. However, out of time order correlators receive other equally important $1/c$ suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on $\lambda_L$ that emerges at large $c$, focusing on CFT$_2$ and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.