Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model

Abstract

We study correlation functions in the one-dimensional $\mathcal{N}=2$ supersymmetric SYK model. The leading order 4-point correlation functions are computed by summing over ladder diagrams expanded in a suitable basis of conformal eigenfunctions. A novelty of the $\mathcal{N}=2$ model is that both symmetric and antisymmetric eigenfunctions are required. Although we use a component formalism, we verify that the operator spectrum and 4-point functions are consistent with $\mathcal{N}=2$ supersymmetry. We also confirm the maximally chaotic behavior of this model and comment briefly on its 6-point functions.

31 pages, 3 figures, v2: several minor typos corrected