The Moduli Space of the $N=2$ Supersymmetric $G_{2}$ Yang-Mills Theory

TL;DR

This paper derives the hyper-elliptic curve for the moduli space of N=2 supersymmetric G2 Yang-Mills theory, determining monodromies and dyon spectrum, and verifies a solitonic equation within this context.

Contribution

It provides the explicit hyper-elliptic curve for the G2 gauge group moduli space and confirms the validity of a recent solitonic equation in this setting.

Findings

Derived the hyper-elliptic curve for G2 moduli space

Determined exact monodromies and dyon spectrum

Verified the solitonic equation for the solution

Abstract

We present the hyper-elliptic curve describing the moduli space of the N=2 supersymmetric Yang-Mills theory with the $G_2$ gauge group. The exact monodromies and the dyon spectrum of the theory are determined. It is verified that the recently proposed solitonic equation is also satisfied by our solution.