Direct Derivation of Scaling Relation of Prepotential in N=2 Supersymmetric G₂ Yang-Mills Theory

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.