Multi-Instanton Calculus and Equivariant Cohomology

TL;DR

This paper develops a systematic method to compute multi-instanton amplitudes in gauge theories using equivariant cohomology and localization, with applications to N=4 and N=2 theories.

Contribution

It introduces a supersymmetric localization approach to derive multi-instanton amplitudes via ADHM equivariant cohomology, advancing computational techniques in gauge theory.

Findings

Derived explicit multi-instanton amplitudes for N=4 and N=2 theories.

Established a supersymmetric localization framework for equivariant forms.

Connected instanton calculus with equivariant cohomology methods.

Abstract

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and N=2 gauge theories with adjoint and fundamental matter.