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 $T_{\mathrm{eff}}\le T$. 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 $2\pi T_{\mathrm{eff}}$, so that scrambling is suppressed by the heavy insertions.

6 pages, 1 figure; v2: minor fixes, updated references

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