Exact superpotentials, theories with flavor and confining vacua -: art. no. 051

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.