From special lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform

Naichung Conan Leung*, Shing Tung Yau, Eric Zaslow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1319-1341
Number of pages23
JournalAdvances in Theoretical and Mathematical Physics
Volume4
Issue number6
DOIs
StatePublished - Nov 2000

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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