Scrambling in nearly thermalized states at large central charge

Abstract

We study $2d$ conformal field theory (CFT) at large central charge $c$ and finite temperature $T$ with heavy operators inserted at spatial infinity. The heavy operators produce a nearly thermalized steady state at an effective temperature $T_{\rm eff}\leq T$. Under some assumptions, we find an effective Schwarzian-like description of these states and, when they exist, their gravity duals. We use this description to compute the Lyapunov exponents for light operators to be $2πT_{\rm eff}$, so that scrambling is suppressed by the heavy insertions.

Figures (1)

• Figure 1: The Hartle-Hawking construction for the two-sided BTZ black brane with nonzero $h, \bar{h}$. Half of the Euclidean geometry \ref{['E:euclideanBTZ']} is glued to the future half of the two-sided black brane across the $t=0$ slice. The thick blue dot represents the defect, the diagonal black lines the horizons, and the dashed red line the future singularity.