Mirror symmetry for Nahm branes

Autor(es)

Franco, Emilio ; Jardim, Marcos

• Tipo de documento: Artigo Científico
• Fonte: EPIJOURNAL DE GEOMETRIE ALGEBRIQUE; v. 6, p. 29-pg., 2022-02-28.

Resumo

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. (AU)

• Processo FAPESP: 12/16356-6 - Fibrados de Higgs sobre curvas elípticas
• Beneficiário: Emilio Franco Gómez
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 16/03759-6 - Espaços de módulos de feixes no espaço projetivo
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 18/21391-1 - Teoria de calibre e geometria algébrica
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Temático