Mirror symmetry with branes by equivariant Verlinde formulae
Algebraic Geometry
2017-12-13 v1 High Energy Physics - Theory
Abstract
We find an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL(2) Higgs moduli space on a Riemann surface. On one side we have the components of the Lagrangian brane of U(1,1) Higgs bundles whose mirror was proposed by Nigel Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL(2) Higgs moduli space. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin's proposal.
Keywords
Cite
@article{arxiv.1712.04408,
title = {Mirror symmetry with branes by equivariant Verlinde formulae},
author = {Tamas Hausel and Anton Mellit and Du Pei},
journal= {arXiv preprint arXiv:1712.04408},
year = {2017}
}
Comments
to appear in Hitchin 70th birthday volume