Correlators in the N = 2 $$ \mathcal{N}=2 $$ supersymmetric SYK model

Abstract

We study correlation functions in the one-dimensional 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 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 N = 2 supersymmetry. We also confirm the maximally chaotic behavior of this model and comment briefly on its 6-point functions.

$$ \mathcal{N}=2 $$ SYK model in the superspace formalism

“…This paper is a logical continuation of [18] and relies heavily on the machinery developed in [6]. We also compare some of our results against [5] and [7] and find them in agreement.…”

“…It has been endowed with extra global symmetry [3,4], supersymmetry [5][6][7], it has been studied as a tensor model with non-random coupling [8,9], also with added supersymmetry [10]. In this paper, we study an N = 2 supersymmetric version of the model, and then generalize further to a two-dimensional theory.…”

“…The N = 2 SYK model has already been studied in [5] and [7]. In this paper, we develop the approach of [5] and work in superspace with chiral and anti-chiral fields.…”

A note on the SYK model with complex fermions

“…We see that for the series of allowed bound states with integer h, the eigenvalues of retarded and conformal kernels are equal: 18) so both h = 2 and h = 0 (or h = 1) modes develop chaotic behavior. In general to find the operators contributing to chaos, we solve the equation:…”

“…While finishing the draft, the author noticed that the paper [18] has considerable overlap with the analysis presented here.…”