Title: Special Lagrangian and deformed Hermitian Yang-Mills on tropical manifold,
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.