Title: From Special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai Transform    
	
Authors: Naichung Conan Leung, Shing-Tung Yau, Eric Zaslow

	
Abstract:

	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 B-cycles. 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.