Black Holes and Random Matrices

TL;DR

This paper explores how the late-time horizon fluctuations of large AdS black holes exhibit quantum chaotic behavior described by random matrix theory, using the SYK model as a key example.

Contribution

It demonstrates that black hole horizon fluctuations follow random matrix dynamics at late times and provides estimates for the crossover time from early to late time behavior.

Findings

Random matrix behavior observed at late times in SYK model

Exact early time behavior determined in a double scaling limit

Provisional estimates for crossover times in large AdS black holes

Abstract

We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function $|Z(\beta +it)|^2$ as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.