One-Instanton Prepotentials from WDVV equations in N=2 Supersymmetric SU(4) Yang-Mills Theory

TL;DR

This paper derives one-instanton prepotentials in N=2 SU(4) supersymmetric Yang-Mills theory directly from WDVV equations, avoiding the need for Seiberg-Witten curves, and finds some match instanton calculus results.

Contribution

It demonstrates that one-instanton prepotentials can be obtained solely from WDVV equations and scaling relations without using Seiberg-Witten curves.

Findings

Derived various one-instanton prepotentials satisfying WDVV and scaling relations.

Identified prepotentials that coincide with instanton calculus results.

Showed that prepotentials can be obtained without Seiberg-Witten curves.

Abstract

Prepotentials in N=2 supersymmetric Yang-Mills theories are known to obey non-linear partial differential equations called Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In this paper, the prepotentials at 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 Seiberg-Witten curve. In this way, various one-instanton prepotentials which satisfy both WDVV equations and scaling relation can be derived, but it turns out that among them there exist one-instanton prepotentials which coincide with the instanton calculus.