On the Multi Trace Superpotential and Corresponding Matrix Model

TL;DR

This paper demonstrates how a matrix model with a linearized potential can reproduce the effective superpotential of an N=1 supersymmetric U(N) gauge theory with a multi-trace superpotential, linking gauge theory and matrix models.

Contribution

It introduces a method to derive the gauge theory superpotential from a matrix model with an auxiliary field, extending the matrix model approach to multi-trace superpotentials.

Findings

Matrix model reproduces gauge theory superpotential.

Effective action matches field theory results.

Auxiliary field integration yields correct superpotential.

Abstract

We study N=1 supersymmetric U(N) gauge theory coupled to an adjoint scalar superfiled with a cubic superpotential containing a multi trace term. We show that the field theory results can be reproduced from a matrix model which its potential is given in terms of a linearized potential obtained from the gauge theory superpotential by adding some auxiliary nondynamical field. Once we get the effective action from this matrix model we could integrate out the auxiliary field getting the correct field theory results.