N=1 Supersymmetric $SU(2)^r$ Moose Theories

TL;DR

This paper investigates the quantum moduli spaces and superpotentials of four-dimensional N=1 supersymmetric SU(2)^r moose theories, revealing nontrivial structures, phase behaviors, and the Seiberg-Witten elliptic curve description.

Contribution

It introduces the analysis of quantum moduli spaces and superpotentials for SU(2)^r moose theories, including the derivation of the Seiberg-Witten curve for the ring configuration.

Findings

Quantum moduli spaces and superpotentials are explicitly constructed.

The ring moose exhibits Coulomb phase with singular submanifolds.

The Seiberg-Witten elliptic curve describes the quantum moduli space.

Abstract

We study the quantum moduli spaces and dynamical superpotentials of four dimensional $SU(2)^r$ linear and ring moose theories with $\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation. Nontrivial quantum moduli spaces and dynamical superpotentials are produced. When the moduli space is perturbed by generic tree level superpotentials, the vacuum space becomes discrete. The ring moose is in the Coulomb phase and we find two singular submanifolds with a nontrivial modulus that is a function of all the independent gauge invariants needed to parameterize the quantum moduli space. The massive theory near these singularities confines. The Seiberg-Witten elliptic curve that describes the quantum moduli space of the ring moose is produced.