ADE Confining Phase Superpotentials

TL;DR

This paper derives a low-energy superpotential for N=1 ADE gauge theories with a confined photon phase, linking Coulomb branch singularities to ADE classifications and exploring connections to N=2 superconformal theories.

Contribution

It provides a novel superpotential formulation for ADE gauge groups in N=1 theories and relates it to N=2 curves and fixed points, extending understanding of gauge theory moduli spaces.

Findings

Superpotential for ADE gauge groups with confined photon phase.

Relation of Coulomb branch singularities to ADE classification.

Insights into N=2 superconformal fixed points and matter inclusion.

Abstract

We obtain a low-energy effective superpotential for a phase with a single confined photon in N=1 gauge theory with an adjoint matter with ADE gauge groups. The expectation values of gauge invariants built out of the adjoint field parametrize the singularities of moduli space of the Coulomb phase. The result can be used to derive the N=2 curve in the form of a foliation over $CP^1$. Our N=1 theory exhibits non-trivial fixed points which naturally inherit the properties of the ADE classification of N=2 superconformal field theories in four dimensions. We also discuss how to include matter hypermultiplets toward deriving the Riemann surface which describes N=2 QCD with exceptional gauge groups.