Supersymmetric SYK model and random matrix theory
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...
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| description | 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. |
| doi_str_mv | 10.48550/arxiv.1702.01738 |
| format | Article |
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| subjects | Classification Form factors Mathematical analysis Mathematical models Matrix methods Matrix theory Physics - High Energy Physics - Theory Physics - Quantum Physics Physics - Statistical Mechanics Supersymmetry Time dependence Two dimensional models |
| title | Supersymmetric SYK model and random matrix theory |
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