Chaotic strings in AdS/CFT

TL;DR

The 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.

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.

Figures (2)

• Figure 1: The setup: a string (shown in red) stretching between the two asymptotic boundaries of an eternal AdS black hole.
• Figure 2: The four-point function (\ref{['DOTOC']}) as an inner product of the two states (\ref{['instate']}) and (\ref{['outstate']}). The solid lines represent spacelike slices of the string world sheet, while the wiggles correspond to operator insertions near the horizons.