Journal Article Black holes and random matrices

Cotler, Jordan S.  ,  Gur-Ari, Guy  ,  Hanada, Masanori  ,  Polchinski, Joseph  ,  Saad, Phil  ,  Shenker, Stephen H.  ,  Stanford, Douglas  ,  Streicher, Alexandre  ,  Tezuka, Masaki

20172017-5 , Springer Nature
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(β + 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.

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