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Families of Hitchin Systems in Type-D

Aswin Balasubramanian, Jacques Distler, Ron Donagi, Carlos Perez-Pardavila

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.

Families of Hitchin Systems in Type-D

Abstract

The Coulomb branch geometry of a 4d 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 on which we compactified from 6d to 4d. As we vary the complex structure of , these fit together to form a (nontrivial!) bundle of Hitchin systems over the moduli space of complex structures of (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.

Paper Structure

This paper contains 48 sections, 1 theorem, 283 equations.

Table of Contents

  1. Introduction
  2. Review
  3. Families of Hitchin systems in Type-A
  4. C₀,ₙ
  5. C₀,₃
  6. C₀,₄
  7. C₀,₅
  8. The local Hitchin base in type-D
  9. The Global Story for Type-D
  10. Global Hitchin base on a smooth curve C
  11. Families of Hitchin bases
  12. The Hitchin system on a fixed curve C
  13. The nilpotent at the node
  14. Imposing the constraints
  15. Even-type constraints --- the easy cases
  16. ...and 33 more sections

Key Result

Proposition 1

Theorems & Definitions (2)

  • Proposition 1
  • Definition 1