Multi-Instanton Calculus in $N=2$ Supersymmetric Gauge Theory

TL;DR

This paper directly analyzes instanton solutions in N=2 supersymmetric SU(2) gauge theory, calculating their contributions to the low-energy effective action and confirming predictions from Seiberg-Witten theory.

Contribution

It provides an explicit construction and analysis of multi-instanton solutions using the ADHM method, and computes their effects on the effective action, matching theoretical predictions.

Findings

Exact classical interactions between n instantons derived

One- and two-instanton contributions match Seiberg-Witten predictions

Detailed behavior of instanton fields at various scales analyzed

Abstract

The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theory may be viewed as a prediction for the infinite family of constants F_n measuring the n-instanton contribution to the prepotential F. Here we examine the instanton physics directly, in particular the contribution of the general self-dual solution of topological charge n constructed by Atiyah, Drinfeld, Hitchin and Manin (ADHM). In both the bosonic and supersymmetric cases, we determine both the large- and short-distance behavior of all the fields in this background. This allows us to construct the exact classical interaction between n ADHM (super-)instantons mediated by the adjoint Higgs. We calculate the one- and two-instanton contributions to the low-energy Seiberg-Witten effective action, and find precise agreement with their predicted values of F_1 and F_2.