N=1 Supersymmetric Product Group Theories in the Coulomb Phase

TL;DR

This work extends the Seiberg-Witten Coulomb-branch program to $N=1$ supersymmetric theories with product gauge groups $SU(N)^M$ and $M$ chiral multiplets transforming under neighboring factors. The low-energy couplings are encoded in hyperelliptic curves of genus $N-1$ (and higher in certain cases), derived by analyzing a range of limits to match known $N=2$ and $N=1$ results, including mass perturbations and Higgsing. The authors provide explicit curves for $SU(2)^N$, $SU(N)\times SU(N)$, and general $SU(N)^M$ theories, and perform nontrivial consistency checks such as confinement, quantum-modified constraints, and vacuum counting (e.g., nine vacua for $N=3$ in the $SU(3)\times SU(3)$ case). A key feature is the appearance of chiral Coulomb-phase dynamics for $M>2$, making these models potentially useful for dynamical supersymmetry breaking model-building; the paper also includes a D-flat analysis confirming the moduli-space structure with residual $U(1)^{N-1}$.

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.