# Supersymmetric SYK model and random matrix theory

## TL;DR

This paper explores how supersymmetry influences the random matrix classification of the SYK model, revealing a new eight-fold symmetry class and analyzing spectral statistics and chaos indicators.

## Contribution

It introduces a supersymmetric generalization of the SYK model, demonstrating a novel eight-fold symmetry classification and analyzing its spectral and chaotic properties.

## Key findings

- Supersymmetric SYK exhibits a distinct eight-fold symmetry classification.
- Spectral form factor shows late-time behavior consistent with random matrix theory.
- Supersymmetry modifies the spectral statistics compared to the original SYK model.

## Abstract

In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the $\mathcal{N}=1$ supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) model, a toy model for the 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 random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. 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.