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arXiv · 1707.09717

Special Lagrangian and deformed Hermitian Yang-Mills on tropical manifold

Hikaru Yamamoto
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Abstract

From string theory, the notion of deformed Hermitian Yang-Mills connections has been introduced by Mari\~no, Minasian, Moore and Strominger. After that, Leung, Yau and Zaslow 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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Hikaru Yamamoto. 2017-07-31. Special Lagrangian and deformed Hermitian Yang-Mills on tropical manifold. https://arxiv.org/abs/1707.09717

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