## Emilio Franco ; Marcos Jardim - Mirror symmetry for Nahm branes

epiga:6604 - Épijournal de Géométrie Algébrique, March 1, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.6604
Mirror symmetry for Nahm branes

Authors: Emilio Franco ; Marcos Jardim

The Dirac--Higgs bundle is a hyperholomorphic bundle over the moduli space of stable Higgs bundles of coprime rank and degree. We provide an algebraic generalization to the case of trivial degree and the rank higher than $1$. This allow us to generalize to this case the Nahm transform defined by Frejlich and the second named author, which, out of a stable Higgs bundle, produces a vector bundle with connection over the moduli space of rank 1 Higgs bundles. By performing the higher rank Nahm transform we obtain a hyperholomorphic bundle with connection over the moduli space of stable Higgs bundles of rank $n$ and degree 0, twisted by the gerbe of liftings of the projective universal bundle. Such hyperholomorphic vector bundles over the moduli space of stable Higgs bundles can be seen, in the physicist's language, as BBB-branes twisted by the above mentioned gerbe. We refer to these objects as Nahm branes. Finally, we study the behaviour of Nahm branes under Fourier--Mukai transform over the smooth locus of the Hitchin fibration, checking that the resulting objects are supported on a Lagrangian multisection of the Hitchin fibration, so they describe partial data of BAA-branes.

Volume: Volume 6
Published on: March 1, 2022
Accepted on: March 1, 2022
Submitted on: June 29, 2020
Keywords: Mathematics - Algebraic Geometry,14D20, 14H60, 14J33