N=1 curves for trifundamentals

TL;DR

This paper investigates the Coulomb phase of a specific N=1 supersymmetric gauge theory with a trifundamental field, revealing that its moduli space is one-dimensional and describing the associated Seiberg-Witten curve as a double cover of a Riemann surface.

Contribution

It provides a novel description of the N=1 Seiberg-Witten curve for SU(2)^3 gauge theory with a trifundamental, using a geometric construction involving branched covers of Riemann surfaces.

Findings

Moduli space is one-dimensional with multiple unbroken U(1)s.

Seiberg-Witten curve is a double cover of a Riemann surface.

Curve is branched at poles and zeros of a meromorphic function.

Abstract

We study the Coulomb phase of N=1 SU(2)^3 gauge theory coupled to one trifundamental field, and generalizations thereof. The moduli space of vacua is always one-dimensional with multiple unbroken U(1) fields. We find that the N=1 Seiberg-Witten curve which encodes the U(1) couplings is given by the double cover of a Riemann surface branched at the poles and the zeros of a meromorphic function.