The Borel subgroup and branes on the Higgs moduli space
Abstract
We consider two families of branes supported on the singular locus of the moduli space of Higgs bundles over a smooth projective curve $X$. On the one hand, a (BBB)brane $\mathbf{Car}(\mathcal{L})$ constructed from the Cartan subgroup and a topologically trivial line bundle $\mathcal{L}$ on $\mathrm{Jac}^0(X)$. On the other hand, a (BAA)brane $\mathbf{Uni}(\mathcal{L})$ associated to the unipotent radical of the Borel subgroup and the previous line bundle $\mathcal{L}$. We give evidence of both branes being dual under mirror symmetry, in the sense that an adhoc FourierMukai integral functor relates the restriction of the hyperholomorphic bundle of the (BBB)brane to a generic Hitchin fibre, with the support of the (BAA)brane. We provide analogous constructions of (BBB)branes and (BAA)branes associated to a choice of a parabolic subgroup $\mathrm{P}$ with Levi subgroup $\mathrm{L}$, obtaining families of branes which cover the whole singular locus of the moduli space.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.03549
 Bibcode:
 2017arXiv170903549F
 Keywords:

 Mathematics  Algebraic Geometry;
 14H60;
 14D21;
 32G13;
 32G81
 EPrint:
 1 figure, Section 6 completed