WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves

TL;DR

This paper derives WDVV equations for 6d Seiberg-Witten theory and extends them to bi-elliptic spectral curves, revealing that elliptization increases the moduli count, enriching the mathematical structure of the theory.

Contribution

It provides a generic derivation of WDVV equations for 6d Seiberg-Witten theory and extends the framework to bi-elliptic spectral curves, highlighting the impact on moduli space.

Findings

Elliptization roughly doubles the number of moduli.

Derived WDVV equations for 6d Seiberg-Witten theory.

Extended analysis to bi-elliptic spectral curves.

Abstract

We present a generic derivation of the WDVV equations for 6d Seiberg-Witten theory, and extend it to the families of bi-elliptic spectral curves. We find that the elliptization of the naive perturbative and nonperturbative 6d systems roughly "doubles" the number of moduli describing the system.