The Coulomb Phase in N=1 Gauge Theories With a LG-Type Superpotenetial

TL;DR

This paper analyzes the Coulomb branch in N=1 supersymmetric gauge theories with specific superpotentials, deriving hyperelliptic curves for low-energy effective couplings and exploring superconformal points.

Contribution

It derives hyperelliptic curves for SO(N_c) and USp(N_c) gauge groups and investigates superconformal points in the Coulomb branch of these theories.

Findings

Hyperelliptic curves encode low-energy gauge couplings.

Identification of vacua with massless dyons.

Analysis of superconformal points at singularities.

Abstract

We consider N=1 supersymmetric gauge theories with a simple classical gauge group, one adjoint $\Phi, N_f$ pairs ($Q_i,\tilde{Q_i}$) of (fundamental, anti-fundamental) and a tree-level superpotential with terms of the Landau-Ginzburg form $\tilde{Q}_i\Phi^lQ_j$. The quantum moduli space of these models includes a Coulomb branch. We find hyperelliptic 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 non-trivial superconformal points appearing when singularities merge in the Coulomb branch.