Central charges, symplectic forms, and hypergeometric series in local mirror symmetry

TL;DR

This paper explores the role of hypergeometric series in local mirror symmetry, linking it to central charges of BPS states and analyzing its monodromy through homological mirror symmetry, with conjectures on symplectic properties.

Contribution

It identifies a hypergeometric series as a central charge formula and conjectures its integral symplectic monodromy in local mirror symmetry.

Findings

Hypergeometric series corresponds to BPS central charges.

Monodromy properties relate to Kontsevich's homological mirror symmetry.

Conjecture of integral symplectic monodromy for hypergeometric series.

Abstract

We study a cohomology-valued hypergeometric series which naturally arises in the description of (local) mirror symmetry. We identify it as a central charge formula for BPS states and study its monodromy property from the viewpoint of Kontsevich's homological mirror symmetry. In the case of local mirror symmetry, we will identify a symplectic form, and will conjecture an integral and symplectic monodromy property of a relevant hypergeometric series of Gel'fand-Kapranov-Zelevinski type.