A Quantum Correction To Chaos

Abstract

We use results on Virasoro conformal blocks to study chaotic dynamics in CFT$_2$ at large central charge c. The Lyapunov exponent $λ_L$, which is a diagnostic for the early onset of chaos, receives $1/c$ corrections that may be interpreted as $λ_L = \frac{2 π}β \left( 1 + \frac{12}{c} \right)$. 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 $λ_L$ 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.

22+6 pages, 6 figures