Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories

TL;DR

This paper uses instanton calculus to verify a nonperturbative relation in N=2 supersymmetric gauge theories, confirming previous results for instantons up to winding number 2.

Contribution

It provides a direct instanton calculus check of a key nonperturbative relation in N=2 supersymmetric gauge theories, extending verification to instantons of winding number 2.

Findings

Agreement with previous nonperturbative results

Verification of the relation for instantons up to k=2

Confirmation of the relation in the weak coupling region

Abstract

Using instanton calculus we check, in the weak coupling region, the nonperturbative relation $$ <\Tr\phi^2>=i\pi\left(\cf-{a\over 2} {\partial\cf\over\partial a}\right)$$ obtained for a N=2 globally supersymmetric gauge theory. Our computations are performed for instantons of winding number k, up to k=2 and turn out to agree with previous nonperturbative results.