A-D-E Singularity and Prepotentials in N=2 Supersymmetric Yang-Mills Theory

TL;DR

This paper computes instanton corrections to the prepotential in N=2 supersymmetric Yang-Mills theories with A-D-E gauge groups using Seiberg-Witten geometry and affine Toda spectral curves, confirming results with microscopic calculations.

Contribution

It provides explicit calculations of instanton corrections for all A-D-E gauge groups using geometric methods, extending previous results.

Findings

Explicit one-instanton contributions derived

Results agree with microscopic instanton calculations

Method applies to all A-D-E gauge groups

Abstract

We calculate the instanton corrections in the effective prepotential for N=2 supersymmetric Yang-Mills theory with all A-D-E gauge groups from the Seiberg-Witten geometry constructed out of the spectral curves of the affine Toda lattice. The one-instanton contribution is determined explicitly by solving the Gauss-Manin system associated with the A-D-E singularity. Our results are in complete agreement with the ones obtained from the microscopic instanton calculations.