Multi-Instanton Check of the Relation Between the Prepotential F and the Modulus u in N=2 SUSY Yang-Mills Theory

TL;DR

This paper performs a multi-instanton analysis in N=2 SUSY SU(2) gauge theory to verify the relationship between the prepotential and the moduli space coordinate, supporting the exact Seiberg-Witten results.

Contribution

It provides a general multi-instanton derivation of the relation between the prepotential and the moduli space coordinate, confirming the exact results in supersymmetric gauge theory.

Findings

Derived the F-u relation to all instanton orders

Confirmed Matone's relation via multi-instanton calculations

Supported the Seiberg-Witten solution with non-perturbative checks

Abstract

By examining multi-instantons in N=2 supersymmetric SU(2) gauge theory, we derive, on very general grounds, and to all orders in the instanton number, a relationship between the prepotential F(Phi), and the coordinate on the quantum moduli space u=<Tr Phi^2>. This relation was previously obtained by Matone in the context of the explicit Seiberg-Witten low-energy solution of the model. Our findings can be viewed as a multi-instanton check of the proposed exact results in supersymmetric gauge theory.