Calculating the Prepotential by Localization on the Moduli Space of Instantons

TL;DR

This paper introduces a localization technique to compute instanton effects in supersymmetric gauge theories, enabling precise calculations of the prepotential and matching predictions from Seiberg-Witten theory.

Contribution

A novel localization method for calculating instanton contributions on constrained moduli spaces in supersymmetric gauge theories.

Findings

Calculated one- and two-instanton contributions to the prepotential.

Demonstrated agreement with Seiberg-Witten predictions.

Extended the approach to arbitrary instanton numbers.

Abstract

We describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton moduli space. Due to existence of a nilpotent fermionic symmetry the resulting integral over the instanton moduli space localizes on the critical points of the potential. Using this technology we calculate the one- and two-instanton contributions to the prepotential of SU(N) gauge theory with N=2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve. The technique appears to extend to arbitrary instanton number in a tractable way.