Central charges in local mirror symmetry via hypergeometric duality

TL;DR

This paper uses hypergeometric systems to analyze toric Calabi-Yau stacks and their mirrors, confirming the equivalence of brane structures and extending the Gamma conjecture to local mirror symmetry.

Contribution

It demonstrates the coincidence of integral structures of A-branes and B-branes in local mirror symmetry using hypergeometric duality, confirming a local version of Hosono's conjecture.

Findings

Integral structures of A-branes and B-branes coincide.

Confirms a local version of Hosono's conjecture.

Generalizes the Gamma conjecture for local mirror symmetry.

Abstract

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 that the integral structures of A-branes and B-branes coincide. This confirms a local version of a conjecture of Hosono and can be seen as a generalization of the Gamma conjecture for local mirror symmetry.