On the Moduli Space of N = 2 Supersymmetric G_2 Gauge Theory

TL;DR

This paper investigates the moduli space of N=2 supersymmetric G_2 gauge theory using confining phase superpotentials, comparing results with spectral curves and extending analysis to theories with fundamental matter.

Contribution

It introduces a novel application of confining phase superpotentials to G_2 gauge theory and clarifies its spectral curve structure, contrasting with previous hyperelliptic curve proposals.

Findings

Results align with the spectral curve of the periodic Toda lattice.

Disagreement with previously suggested hyperelliptic curves.

Extended analysis to theories with fundamental matter, including SO(5) and G_2.

Abstract

We apply the method of confining phase superpotentials to N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G_2. Our findings are consistent with the spectral curve of the periodic Toda lattice, but do not agree with the hyperelliptic curve suggested previously in the literature. We also apply the method to theories with fundamental matter, treating both the example of SO(5) and G_2.