Confining Phase of N=1 Supersymmetric Gauge Theories and N=2 Massless Solitons

TL;DR

This paper derives effective superpotentials for confining phases in N=1 supersymmetric gauge theories, extends hyperelliptic curve descriptions to N=2 theories with classical gauge groups, and identifies new N=1 superconformal theories.

Contribution

It extends the hyperelliptic curve framework to N=2 theories with classical gauge groups and finds new N=1 superconformal field theories by tuning superpotentials.

Findings

Derived superpotentials for confining phases.

Extended hyperelliptic curves to N=2 theories with classical groups.

Discovered new N=1 superconformal theories.

Abstract

Effective superpotentials for the phase with a confined photon are obtained in $N=1$ supersymmetric gauge theories. We use the results to derive the hyperelliptic curves which describe the Coulomb phase of $N=2$ theories with classical gauge groups, and thus extending the prior result for $SU(N_c)$ gauge theory by Elitzur et al. Moreover, adjusting the coupling constants in $N=1$ effective superpotentials to the values of $N=2$ non-trivial critical points we find new classes of $N=1$ superconformal field theories with an adjoint matter with a superpotential.