Central charges of T-dual branes for toric varieties

Abstract

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

arXiv comment21 page, 3 figures

References in corpus (9)

• A New Cohomology Theory for Orbifold
• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Topological Orbifold Models and Quantum Cohomology Rings
• A Mirror Theorem for Toric Stacks
• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• The nonequivariant coherent-constructible correspondence for toric stacks
• The Eynard-Orantin recursion and equivariant mirror symmetry for the projective line
• Remarks on the nonequivariant coherent-constructible correspondence for toric varieties
• Seidel Representations and Quantum Cohomology of Toric Orbifolds

Cited by in corpus (4)

• Reconstructing GKZ via topological recursion
• Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry
• Reconstruction of $T_{{\mathbb{P}}^2}$ via tropical Lagrangian multi-section
• Equivariant mirror symmetry for the weighted projective line