A note on instanton counting for N=2 gauge theories with classical gauge groups

TL;DR

This paper computes the prepotential of N=2 SO and Sp gauge theories using instanton counting, providing explicit formulas and comparisons with Seiberg-Witten predictions, advancing understanding of these theories' non-perturbative aspects.

Contribution

It offers a closed-form expression for the prepotential of SO theories and detailed instanton calculations for Sp theories, extending instanton counting techniques to classical gauge groups.

Findings

Closed-form prepotential for SO theories without matter.

Prepotential calculations up to third instanton for Sp theories.

Validation of results against Seiberg-Witten geometries.

Abstract

We study the prepotential of N=2 gauge theories using the instanton counting techniques introduced by Nekrasov. For the SO theories without matter we find a closed expression for the full prepotential and its string theory gravitational corrections. For the more subtle case of Sp theories without matter we discuss general features and compute the prepotential up to instanton number three. We also briefly discuss SU theories with matter in the symmetric and antisymmetric representations. We check all our results against the predictions of the corresponding Seiberg-Witten geometries.