Supersymmetric SYK model and random matrix theory

Abstract

In this paper, we discuss random matrix behaviors in the \(\mathcal{N}=1\) supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as standard Dyson ensembles, with a different eight-fold classification from the original SYK model. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic Hamiltonian with supersymmetry.