Baryons, Boundaries and Matrix Models

TL;DR

This paper extends the gauge theory-matrix model duality to include fundamental and baryonic operators, analyzing the effective superpotential and moduli space of vacua using field theory techniques.

Contribution

It introduces a field theory analysis of gauge theories with multi-trace operators and extends the duality to include baryonic operators and fundamental matter.

Findings

Effective superpotential generated by planar diagrams with at most one boundary.

Full moduli space of vacua for U(N) with N flavors obtained.

Program outlined for string theory justification of the duality.

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.