Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation

Abstract

We discuss the bi-local collective theory for the $\mathcal{N}=1,2$ supersymmetric Sachdev-Ye-Kitaev (SUSY SYK) models. We construct a bi-local superspace, and formulate the bi-local collective superfield theory of the one-dimensional SUSY vector model. The bi-local collective theory provides systematic analysis of the SUSY SYK models. We find that this bi-local collective theory naturally leads to supermatrix formulation in the bi-local superspace. This supermatrix formulation drastically simplifies the analysis of the SUSY SYK models. We also study $\mathcal{N}=1$ bi-local superconformal generators in the supermatrix formulation, and find the eigenvectors of teh superconformal Casimir. We diagonalize the quadratic action in large $N$ expansion.

48 page; v2:typo corrected, reference added, notation for the eigenfunctions changed

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Cited by in corpus (9)

• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• SYK Model, Chaos and Conserved Charge
• Phases Of Melonic Quantum Mechanics
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• SYK Model with global symmetries in the double scaling limit
• A route from maximal chaoticity to integrability