Title: Supersymmetric SYK model and random matrix theory Show Chinese title

Title: 超对称SYK模型和随机矩阵理论

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. Show Chinese abstract

Abstract: 本文研究了超对称性对随机矩阵理论系综对称分类的影响。我们主要关注 Sachdev-Ye-Kitaev (SYK) 模型的超对称推广（即$\mathcal{N}=1$）中随机矩阵的行为，该模型是带有超对称约束的二维量子黑洞的玩具模型。通过一些解析论证和数值结果表明，超对称SYK模型的统计特性可以被解释为随机矩阵理论系综，并且与原始SYK模型具有不同的八重分类以及一些新特征。此外，还研究了谱函数因子的时间演化，其中随机矩阵理论的预测控制着具有超对称性的混沌哈密顿量的晚期行为。