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.
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Yoon, J. Supersymmetric SYK model: bi-local collective superfield/supermatrix formulation. J. High Energ. Phys. 2017, 172 (2017). https://doi.org/10.1007/JHEP10(2017)172
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DOI: https://doi.org/10.1007/JHEP10(2017)172