2016/11/30 by Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada +6 · 1 voice · 2 citations
Physics and Astronomy · #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep05(2017)118
published as JHEP 1705:118, 2017 · 73 pages, 15 figures, minor errors corrected
arxiv created 2018/08/28 · arxiv updated 2018/08/29
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.