From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform.
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Publication:700556
DOI10.4310/ATMP.2000.V4.N6.A5zbMATH Open1033.53044arXivmath/0005118OpenAlexW1804902553WikidataQ57258757 ScholiaQ57258757MaRDI QIDQ700556
Author name not available (Why is that?)
Publication date: 22 October 2002
Published in: (Search for Journal in Brave)
Abstract: We 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.
Full work available at URL: https://arxiv.org/abs/math/0005118
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