Non-perturbative corrections in the semi-classical limit of double-scaled SYK

TL;DR

This paper investigates non-perturbative effects in the double-scaled SYK model's partition function at small coupling, revealing resummation via Dedekind eta functions and exploring potential bulk dual interpretations.

Contribution

It uncovers non-perturbative corrections in DSSYK and demonstrates their resummation using Dedekind eta functions, providing insights into the model's low-temperature behavior.

Findings

Non-perturbative corrections are present in the DSSYK partition function.

These corrections can be resummed by the cubic power of the Dedekind eta function.

Discussion of a possible bulk interpretation of the non-perturbative effects.

Abstract

We study the disk partition function of double-scaled SYK model (DSSYK) in the small $\lambda$ limit, where $\lambda=-\log q$ is the coupling of DSSYK. We find that the partition function receives non-perturbative corrections in $\lambda$, which can be resummed by the cubic power of the Dedekind eta function in a certain low temperature limit. We also discuss a possible bulk interpretation of our findings.