From Special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai Transform

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dc.creatorLeung, Naichung Conan
dc.creatorYau, Shing-Tung
dc.creatorZaslow, Eric
dc.date2000-05-11
dc.date.accessioned2026-07-07T04:35:12Z
dc.date.available2026-07-07T04:35:12Z
dc.descriptionWe exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the transformation relates supersymmetric A- and B-cycles. In this paper, we assume that the mirror pair are dual torus fibrations with flat tori and that the A-cycle is a section. We also show that this transformation preserves the (holomorphic) Chern-Simons functional for all connections. Furthermore, on corresponding moduli spaces of supersymmetric cycles it identifies the graded tangent spaces and the holomorphic m-forms. In particular, we verify Vafa's mirror conjecture with bundles in this special case.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0005118
dc.identifierhttp://arxiv.org/abs/math/0005118
dc.identifierAdv.Theor.Math.Phys. 4 (2002) 1319-1341
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59177
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectSymplectic Geometry
dc.titleFrom Special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai Transform
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