Exact Superpotentials for Theories with Flavors via a Matrix Integral

TL;DR

This paper extends the Dijkgraaf-Vafa matrix model method to include flavors, computing exact superpotentials for specific N=1 theories and confirming results with traditional field theory calculations.

Contribution

It introduces a way to incorporate fundamental flavors into matrix model computations of superpotentials, providing exact results and validation against field theory.

Findings

Exact superpotential computed for U(N_c) with flavors and adjoint

Perfect agreement with traditional field theory calculations

Method extends matrix model techniques to flavored theories

Abstract

We extend and test the method of Dijkgraaf and Vafa for computing the superpotential of N=1 theories to include flavors in the fundamental representation of the gauge group. This amounts to computing the contribution to the superpotential from surfaces with one boundary in the matrix integral. We compute exactly the effective superpotential for the case of gauge group U(N_c), N_f massive flavor chiral multiplets in the fundamental and one massive chiral multiplet in the adjoint, together with a Yukawa coupling. We compare up to sixth-order with the result obtained by standard field theory techniques in the already non trivial case of N_c=2 and N_f=1. The agreement is perfect.