Fine-Grained Chaos in $Ad{S}_2$ Gravity

Abstract

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time ${\hat{u}}_{\ast }$. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes $Ad{S}_2$ gravity and the low-energy dynamics of the SYK model. We identify a particular set of $2k$-point functions, characterized as being both "maximally braided" and "k-OTO", which exhibit exponential growth until progressively longer timescales ${\hat{u}}_{\ast }^{(k)}=(k-1){\hat{u}}_{\ast }$. We suggest an interpretation as scrambling of increasingly fine-grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

8 pages; v2: minor clarifications, typos, added refs

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