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Special Lagrangian and deformed Hermitian Yang–Mills on tropical manifold

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Abstract

From string theory, the notion of deformed Hermitian Yang–Mills connections has been introduced by Mariño et al. (J High Energy Phys Paper 5, 2000). After that, Leung et al. (Adv Theor Math Phys 4(6):1319–1341, 2000) proved that it naturally appears as mirror objects of special Lagrangian submanifolds via Fourier–Mukai transform between dual torus fibrations. In their paper, some conditions are imposed for simplicity. In this paper, data to glue their construction on tropical manifolds are proposed and a generalization of the correspondence is proved without the assumption that the Lagrangian submanifold is a section of the torus fibration.

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Acknowledgements

This work was based on private communications with Professor A. Futaki, so the author would like to thank him for many suggestions and stimulating discussions. The author also would like to thank the reviewers for their careful reading to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Hikaru Yamamoto

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  1. Hikaru Yamamoto
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Correspondence to Hikaru Yamamoto.

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This work was supported by JSPS KAKENHI Grant number 16H07229.

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Yamamoto, H. Special Lagrangian and deformed Hermitian Yang–Mills on tropical manifold. Math. Z. 290, 1023–1040 (2018). https://doi.org/10.1007/s00209-018-2050-0

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  • DOI: https://doi.org/10.1007/s00209-018-2050-0

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