Supersymmetric SYK model: bi-local collective superfield/supermatrix formulation

Abstract

We discuss the bi-local collective theory for the 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 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.