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

Conan Leung Chinese Univ of HK Shing Tung Yau Harvard University Eric Zaslow Northwestern Univ

Differential Geometry mathscidoc:1608.10097

Adv. Theor. Math. Phys. , 4, (6), 1319-1341, 2000
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 Bcycles. 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.
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@inproceedings{conan2000from,
  title={From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform},
  author={Conan Leung, Shing Tung Yau, and Eric Zaslow},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831170242780917581},
  booktitle={Adv. Theor. Math. Phys. },
  volume={4},
  number={6},
  pages={1319-1341},
  year={2000},
}
Conan Leung, Shing Tung Yau, and Eric Zaslow. From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform. 2000. Vol. 4. In Adv. Theor. Math. Phys. . pp.1319-1341. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831170242780917581.
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