One-instanton prepotentials from WDVV equations in N=2 supersymmetric SU(4) Yang–Mills theory

Abstract

Prepotentials in N=2 supersymmetric Yang–Mills theories are known to obey nonlinear partial differential equations called Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. In this paper, the prepotentials at the one-instanton level in N=2 supersymmetric SU(4) Yang–Mills theory are studied from the standpoint of WDVV equations. Especially, it is shown that the one-instanton prepotentials are obtained from WDVV equations by assuming the perturbative prepotential and by using the scaling relation as a subsidiary condition but are determined without introducing the Seiberg–Witten curve. In this way, various one-instanton prepotentials which satisfy both WDVV equations and the scaling relation can be derived, but it turns out that among them there exist one-instanton prepotentials which coincide with the instanton calculus.