On Exact Superpotentials, Free Energies and Matrix Models

TL;DR

This paper derives exact nonperturbative superpotentials for certain supersymmetric gauge theories using matrix models, providing a bridge between gauge theory and matrix model techniques.

Contribution

It presents a method to compute exact superpotentials and free energies in supersymmetric gauge theories via matrix models, including the Veneziano-Yankielowicz term.

Findings

Exact superpotentials obtained from matrix models.

Demonstration of integrating in and out techniques for large N matrix integrals.

Connection established between gauge theories and zero-dimensional matrix models.

Abstract

We discuss exact results for the full nonperturbative effective superpotentials of four dimensional $\mathcal{N}=1$ supersymmetric U(N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large $N$ limit.