On the Picard-Fuchs equations of the SW models

TL;DR

This paper derives explicit Picard-Fuchs equations for N=2 supersymmetric Yang-Mills theories with classical gauge groups, providing series solutions in the semi-classical regime, advancing understanding of their mathematical structure.

Contribution

It presents the closed-form Picard-Fuchs equations for these theories, including regular and exceptional cases, and describes their series solutions.

Findings

Derived explicit Picard-Fuchs equations for classical gauge groups

Identified regular and exceptional differential equations based on rank

Provided series solutions in the semi-classical regime

Abstract

We obtain the closed form of the Picard-Fuchs equations for $N=2$ supersymmetric Yang-Mills theories with classical Lie gauge groups. For a gauge group of rank $r$, there are $r-1$ regular and an exceptional differential equations. We describe the series solutions of the Picard-Fuchs equations in the semi-classical regime.