Central charges in local mirror symmetry via hypergeometric duality

We apply the better-behaved GKZ hypergeometric systems to study toric Calabi-Yau Deligne-Mumford stacks and their Hori-Vafa mirrors given by affine hypersurfaces in algebraic tori. We show the equality between A-model and B-model central charges, in terms of period integrals and hypergeometric series respectively. This settles a conjecture of Hosono, which could also be considered as a generalization of the Gamma conjecture for local mirror symmetry.