Abstract. Maldacena suggested that the late-time behavior of the correlation functions can diagnose the discrete energy spectrum of the black hole microstates. In order to determine such long-time property in the quantum field theories dual to black holes, we consider the Sachdev-Ye-Kitaev (SYK) model as an ideal toy model. We study the correlation functions and the spectral form factor, which is essentially the analytic continuation of the thermal partition function to the Minkowski time, and numerically demonstrate that the long-time behavior of the spectral form factor of the SYK model is reproduced by the Random Matrix Theory (RMT). We argue that super Yang-Mills theory would exhibit the same property, and comment on possible implications to quantum gravity.

This talk is based on a recent paper arXiv: 1611.04650 [hep-th], with J. Cotler, G. Gur-Ari, J. Polchinski, P. Saad, S. Shenker, D. Stanford, A. Streicher and M. Tezuka.