# Correlation functions in ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory

## TL;DR

This paper computes correlation functions in ${
m ext{N}=2}$ supersymmetric Chern-Simons theory at large N, revealing that certain four-point functions resemble free theory results with specific modifications, and analyzing their structure via bootstrap and Schwinger-Dyson methods.

## Contribution

It provides explicit calculations of two- and three-point functions and novel insights into four-point functions, highlighting the contact term nature and exchange contributions in the supersymmetric Chern-Simons context.

## Key findings

- Two- and three-point functions computed at all orders of 't Hooft coupling.
- Four-point function of $J_0^{f}$ resembles free theory up to coupling-dependent factors.
- $J_0^{b}$ four-point function includes additional exchange contributions.

## Abstract

We compute the two, three point function of the opearators in the spin zero multiplet of ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory at large $N$ and at all orders of 't Hooft coupling by solving the Schwinger-Dyson equation. Schwinger-Dyson method to compute four point function becomes extremely complicated and hence we use bootstrap method to solve for four point function of scaler operator $J_0^{f}=\bar\psi \psi$ and $J_0^{b}=\bar\phi \phi$. Interestingly, due to the fact that $\langle J_0^{f}J_0^{f}J_0^{b} \rangle$ is a contact term, the four point function of $ J_0^{f}$ operator looks like that of free theory up to overall coupling constant dependent factors and up to some bulk AdS contact terms. On the other hand the $J_0^{b}$ four-point function receives an additional contribution compared to the free theory expression due to the $J_0^{f}$ exchange. Interestingly, double discontinuity of this single trace operator $J_0^{f}$ vanishes and hence it only contributes to AdS-contact term.