N=2 supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy

TL;DR

This paper integrates N=2 supersymmetric gauge theories with massive hypermultiplets into the Whitham hierarchy, providing new derivative expressions of the prepotential using Riemann theta functions and validating them through duality and semiclassical checks.

Contribution

It extends the Seiberg-Witten solution by embedding it into the Whitham hierarchy and deriving new formulas for prepotential derivatives involving Riemann theta functions.

Findings

Derived first and second derivatives of the prepotential in terms of Riemann theta functions.

Validated the new equations through duality transformation behavior.

Ensured consistency with semiclassical expansions.

Abstract

We embed the Seiberg-Witten solution for the low energy dynamics of N=2 super Yang-Mills theory with an even number of massive hypermultiplets into the Whitham hierarchy. Expressions for the first and second derivatives of the prepotential in terms of the Riemann theta function are provided which extend previous results obtained by Gorsky, Marshakov, Mironov and Morozov. Checks in favour of the new equations involve both their behaviour under duality transformations and the consistency of their semiclassical expansions.