Chaotic strings in AdS/CFT

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 $λ_L=2π/β$. However, the scrambling time is parametrically smaller than for plasma excitations, $t_*\simβ\log \sqrtλ$ instead of $t_*\simβ\log N^2$. 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.

v3: minor additions and typos corrected. Version to appear in PRL