Direct Derivation of Scaling Relation of Prepotential in N=2 Supersymmetric G_2 Yang-Mills Theory

TL;DR

This paper introduces a direct method using Picard-Fuchs equations to prove the scaling relation between moduli and prepotential in N=2 supersymmetric G_2 Yang-Mills theory, confirming previous findings.

Contribution

It provides the first direct proof of the scaling relation for exceptional gauge groups, specifically G_2, using Picard-Fuchs equations.

Findings

The scaling relation in G_2 theory holds exactly.

The method can potentially be applied to other exceptional groups.

Confirms previous conjectures about the G_2 prepotential.

Abstract

In contrast with the classical gauge group cases, any method to prove exactly the scaling relation which relates moduli and prepotential is not known in the case of exceptional gauge groups. This paper provides a direct method to establish this relation by using Picard-Fuchs equations. In particular, it is shown that the scaling relation found by Ito in N=2 supersymmetric G_2 Yang-Mills theory actually holds exactly.