A semiclassical ramp in SYK and in gravity
Abstract
In finite entropy systems, real-time partition functions do not decay to zero at late time. Instead, assuming random matrix universality, suitable averages exhibit a growing "ramp" and "plateau" structure. Deriving this non-decaying behavior in a large collective field description is a challenge related to one version of the black hole information problem. We describe a candidate semiclassical explanation of the ramp for the SYK model and for black holes. In SYK, this is a two-replica nonperturbative saddle point for the large collective fields, with zero action and a compact zero mode that leads to a linearly growing ramp. In the black hole context, the solution is a two-sided black hole that is periodically identified under a Killing time translation. We discuss but do not resolve some puzzles that arise.
Cite
@article{arxiv.1806.06840,
title = {A semiclassical ramp in SYK and in gravity},
author = {Phil Saad and Stephen H. Shenker and Douglas Stanford},
journal= {arXiv preprint arXiv:1806.06840},
year = {2019}
}
Comments
34 pages plus appendices. v2: coefficient of ramp computed (appendix C), minor corrections, references added