N=2 Curves and a Coulomb Phase in N=1 SUSY Gauge Theories with Adjoint and Fundamental Matters

Abstract

We study low-energy effective superpotentials for the phase with a confined photon in N=1 supersymmetric gauge theories with an adjoint matter $\Phi$ and fundamental flavors $Q, \tilde Q$. Arbitrary classical gauge groups are considered. The results are used to derive the hyperelliptic curves which describe the Coulomb phase of N=2 supersymmetric QCD with classical gauge groups. These curves are in agreement with those proposed earlier by several authors. Our results also produce the curves relevant to describe the Coulomb phase of N=1 theories with a superpotential of the form $\tilde{Q} \Phi^{l} Q$.