Chaotic strings in AdS/CFT

TL;DR

This paper investigates chaos in holographic theories, showing that maximal chaos can occur in probe sectors without gravitational degrees of freedom, demonstrated through a Brownian particle model.

Contribution

It demonstrates that maximal chaos, characterized by the Lyapunov exponent, can appear outside the gravitational sector in holographic setups, specifically in a probe particle model.

Findings

Four-point OTO correlator grows exponentially with maximal Lyapunov exponent.

Scrambling time is parametrically smaller than in plasma excitations.

Maximal chaos can occur without explicit gravitational degrees of freedom.

Abstract

Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos. It is interesting to ask whether this property is true only for leading large $N$ correlators or if it can show up elsewhere. In this Letter we consider the simplest setup to tackle this question: a Brownian particle coupled to a thermal ensemble. We find that the four-point out-of-time-order correlator that diagnoses chaos initially grows at an exponential rate that saturates the chaos bound, i.e., with a Lyapunov exponent $\lambda_L=2\pi/\beta$. However, the scrambling time is parametrically smaller than for plasma excitations, $t_*\sim\beta \log \sqrt{\lambda}$ instead of $t_*\sim\beta \log N^2$. Our result shows that, at least in certain cases, maximal chaos can be attained in the probe sector without the explicit need of gravitational degrees of freedom.