Affiliation:
1. Centro de Análise Matemática Geometria e Sistemas Dinâmicos Instituto Superior Técnico Universidade de Lisboa Lisboa Portugal
2. School of Mathematics University of Birmingham Edgbaston Birmingham UK
Abstract
AbstractWe study the mirror symmetry on the singular locus of the Hitchin system at two levels. First, 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. Second, 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.
Funder
Fundação de Amparo à Pesquisa do Estado de São Paulo
Fundação para a Ciência e a Tecnologia
H2020 European Research Council
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