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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 $N$ 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 saddle point for the large $N$ 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. (Work in progress
with Phil Saad and Douglas Stanford.) |
