Families of Hitchin Systems in Type-D

TL;DR

This paper explores the complex structure of Hitchin systems of type D in the context of 4d $ $N=2 SCFTs, revealing how local constraints at punctures influence the global spectral curve structure.

Contribution

It extends the understanding of Hitchin systems in class-S theories to type D, analyzing the impact of local constraints on the global spectral curve bundle.

Findings

Detailed analysis of local constraints at punctures in type-D Hitchin systems

Implications for the global bundle of spectral (Seiberg-Witten) curves

Comparison with the type-A case highlighting increased complexity

Abstract

The Coulomb branch geometry of a 4d $\mathcal{N}=2$ SCFT is encoded in the data of a complex integrable system. In class-S, this is the Hitchin System (of ADE type) on the punctured curves $C$ on which we compactified from 6d to 4d. As we vary the complex structure of $C$, these fit together to form a (nontrivial!) bundle of Hitchin systems over the moduli space of complex structures of $C$ (the ``conformal manifold'' of the family of SCFTs). We carry out that construction for type-D. Compared to the type-A case, the construction is much more complicated because of local constraints at the punctures. Those local constraints were studied in [1]. Here, we work out their implications for the global bundle of spectral (Seiberg-Witten) curves.