Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups

Emilio Franco, Ana Peón-Nieto

Research output: Contribution to journalArticlepeer-review

Abstract

We study mirror symmetry on the singular locus of the Hitchin system at two levels. Firstly, by covering it by (supports of) (BBB)-branes, corresponding to Higgs bundles reducing their structure group to the Levi subgroup of some parabolic subgroup P, whose conjectural dual (BAA)-branes we describe. Heuristically speaking, the latter are given by Higgs bundles reducing their structure group to the unipotent radical of P. Secondly, when P is a Borel subgroup, we are able to construct a family of hyperholomorphic bundles on the (BBB)-brane, and study the variation of the dual under this choice. We give evidence of both families of branes being dual under mirror symmetry via an integral functor induced by Fourier-Mukai in the moduli stack of Higgs bundles.
Original languageEnglish
JournalMathematische Nachrichten
Publication statusAccepted/In press - 24 Feb 2022

Bibliographical note

Not yet published as of 09/05/2022.

Keywords

  • Higgs bundles
  • Branes
  • Mirror symmetry

Fingerprint

Dive into the research topics of 'Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups'. Together they form a unique fingerprint.

Cite this