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

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.