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

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 $\mathrm{P}$, 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 $\mathrm{P}$. Secondly, when $\mathrm{P}$ 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.

1 figure, Greately improved

References in corpus (10)

• Existence of moduli spaces for algebraic stacks
• Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
• Cayley and Langlands type correspondences for orthogonal Higgs bundles
• Unramified covers and branes on the Hitchin system
• Involutions of the moduli spaces of $G$-Higgs bundles over elliptic curves
• Higgs bundles, Lagrangians and mirror symmetry
• Mirror symmetry for Nahm branes
• Orthogonal Higgs bundles with singular spectral curves
• Construction of the Poincare sheaf for higher genus curves
• Construction of the Poincaré sheaf on the stack of rank two Higgs bundles of ${\mathbf{P}}^1$

Cited by in corpus (5)

• Singular Geometry and Higgs Bundles in String Theory
• Unramified covers and branes on the Hitchin system
• Higgs bundles, Lagrangians and mirror symmetry
• Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties
• Fixed point branes, singular loci and mirror symmetry