Baryons, Boundaries and Matrix Models

Abstract

A natural extension of the Dijkgraaf-Vafa proposal is to include fields in the fundamental representation of the gauge group. In this paper we use field theory techniques to analyze gauge theories whose tree level superpotential is a generic polynomial in multi-trace operators constructed out of such fields. We show that the effective superpotential is generated by planar diagrams with at most one (generalized) boundary. This justifies the proposal put forward in hep-th/0211075. We then proceed to extend the gauge theory-matrix model duality to include baryonic operators. We obtain the full moduli space of vacua for an U(N) theory with N flavors. We also outline a program leading to a string theory justification of the gauge theory-matrix model correspondence with fundamental matter.