Central charges of T-dual branes for toric varieties

Abstract

Given any equivariant coherent sheaf L \mathcal {L} on a compact semi-positive toric orbifold X \mathcal {X} , its SYZ T-dual mirror dual is a Lagrangian brane in the Landau-Ginzburg mirror. We prove that the oscillatory integral of the equivariant superpotential in the Landau Ginzburg mirror over this Lagrangian brane is the genus-zero 1 1 -descendant Gromov-Witten potential with a Gamma-type class of L \mathcal {L} inserted.