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

TL;DR

This paper employs superspace techniques to analyze an $ =2$ supersymmetric SYK-like model in one and two dimensions, deriving four-point functions, retarded kernels, and Lyapunov exponents to understand its chaotic behavior.

Contribution

It introduces a superspace formalism for $ =2$ SYK models and computes key correlation functions and chaos indicators in both one and two dimensions.

Findings

Derived four-point functions using $su(1,1|1)$ Casimir eigenfunctions

Calculated retarded kernels and Lyapunov exponents for the models

Extended analysis from one to two dimensions

Abstract

We use superspace methods to study an SYK-like model with $\mathcal N=2$ supersymmetry in one dimension, and an analog of this model in two dimensions. We find the four-point function as an expansion in the basis of eigenfunctions of the Casimir of $su(1,1|1)$. We also find retarded kernels and Lyapunov exponents for both cases.