Ringdown in the SYK model

TL;DR

This paper studies thermal correlators in the SYK model away from maximal chaos, revealing a discrete spectrum of quasinormal modes and a tree-like structure reminiscent of black hole physics.

Contribution

It analytically computes the quasinormal mode spectrum in the SYK model beyond the maximally chaotic limit, using perturbation theory and numerical fitting.

Findings

Spectrum decomposes into discrete quasinormal modes.

Spectrum exhibits a tree-like structure similar to black holes.

Toy model reproduces qualitative features of the spectrum.

Abstract

We analyze thermal correlators in the Sachdev-Ye-Kitaev model away from the maximally chaotic limit. Despite the absence of a weakly curved black hole dual, the two point function decomposes into a sum over a discrete set of quasinormal modes. To compute the spectrum of modes, we analytically solve the Schwinger-Dyson equations to a high order in perturbation theory, and then numerically fit to a sum of exponentials using a technique analogous to the double cone construction. The resulting spectrum has a tree-like structure which is reminiscent of AdS black holes with curvature singularities. We present a simple toy model of stringy black holes that qualitatively reproduces some aspects of this structure.