Special Lagrangian and deformed Hermitian Yang-Mills on tropical manifold

2017/07/31 by Hikaru Yamamoto, Yamamoto, Hikaru
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1707.09717

openalex publication_date 2017/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

From string theory, the notion of deformed Hermitian Yang-Mills connections has been introduced by Mariño, 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.

Citations

• (1,1) forms with specified Lagrangian phase: A priori estimates and\n algebraic obstructions
• Calibrated geometries

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