Exact superpotentials in N=1 theories with flavor and their matrix model formulation

TL;DR

This paper presents a matrix model approach to exactly compute the effective superpotential of N=1 SU(N_c) gauge theories with flavors, successfully reproducing known results and extending to new regimes.

Contribution

It introduces a matrix model prescription that captures the superpotential for N=1 theories with flavors, including cases with N_f > N_c, aligning with known gauge theory dynamics.

Findings

Reproduces the Affleck-Dine-Seiberg superpotential for N_f < N_c

Proposes a matrix model method that accounts for theories with N_f > N_c

Demonstrates exact agreement with gauge theory physics across all N_f and N_c

Abstract

In this note we investigate the effective superpotential of an N=1 SU(N_c) gauge theory with one adjoint chiral multiplet and N_f fundamental chiral multiplets. We propose a matrix model prescription in which only matrix model diagrams with less than two boundaries contribute to the gauge theory effective superpotential. This prescription reproduces exactly the known gauge theory physics for all N_f and $N_c$. For N_f < N_c this is given by the Affleck-Dine-Seiberg superpotential. For N_f > N_c we present arguments leading to the conclusion that the dynamics of these theories is also reproduced by the matrix model.