Exact Superpotentials, Theories with Flavor and Confining Vacua

TL;DR

This paper uses the Dijkgraaf--Vafa matrix model approach to compute exact superpotentials in N=1 supersymmetric gauge theories with fundamental matter, revealing relations to pure gauge theories and analyzing confining vacua.

Contribution

It introduces a method to calculate the effective superpotential for theories with fundamental flavors using pure gauge theory data, including at confining vacua.

Findings

Superpotential for theories with N_f flavors expressed via pure gauge theory

Exact superpotential computed at confining vacua with maximal monopole masslessness

General method extended to arbitrary points in the moduli space

Abstract

In this paper we study some interesting properties of the effective superpotential of N=1 supersymmetric gauge theories with fundamental matter, with the help of the Dijkgraaf--Vafa proposal connecting supersymmetric gauge theories with matrix models. We find that the effective superpotential for theories with N_f fundamental flavors can be calculated in terms of quantities computed in the pure (N_f=0) gauge theory. Using this property we compute in a remarkably simple way the exact effective superpotential of N=1 supersymmetric theories with fundamental matter and gauge group SU(N_c), at the point in the moduli space where a maximal number of monopoles become massless (confining vacua). We extend the analysis to a generic point of the moduli space, and show how to compute the effective superpotential in this general case.