N=1 Supersymmetric Product Group Theories in the Coulomb Phase

TL;DR

This paper investigates the low-energy dynamics of N=1 supersymmetric gauge theories with product gauge groups, deriving hyperelliptic curves to describe their Coulomb phase and confirming their consistency through various limits.

Contribution

The authors derive hyperelliptic curves for N=1 supersymmetric product group theories in the Coulomb phase, providing a new geometric description and consistency checks for these models.

Findings

Hyperelliptic curves describe the low-energy gauge kinetic functions.

Theories are in the Coulomb phase with unbroken U(1)^(N-1).

Consistency checks include confinement and mass perturbations.

Abstract

We study the low-energy behavior of N=1 supersymmetric gauge theories with product gauge groups SU(N)^M and M chiral superfields transforming in the fundamental representation of two of the SU(N) factors. These theories are in the Coulomb phase with an unbroken U(1)^(N-1) gauge group. For N >= 3, M >= 3 the theories are chiral. The low-energy gauge kinetic functions can be obtained from hyperelliptic curves which we derive by considering various limits of the theories. We present several consistency checks of the curves including confinement through the addition of mass perturbations and other limits.