The Coulomb phase in N = 1 gauge theories with an LG-type superpotential

Abstract

We consider N = 1 supersymmetric gauge theories with a simple classical gauge group, one adjoint Φ, N f pairs ( Q i , ∼ Q i ) of (fundamental, anti-fundamental) and a tree-level superpotential with terms of the Landau-Ginzburg form Q iΦ lQ j . The quantum moduli space of these models includes a Coulomb branch. We find hyper-elliptic curves that encode the low energy effective gauge coupling for the groups SO( N c ) and USp( N c ) (the corresponding curve for SU( N c ) is already known). As a consistency check, we derive the sub-space of some vacua with massless dyons via confining phase superpotentials. We also discuss the existence and nature of the nontrivial superconformal points appearing when singularities merge in the Coulomb branch.