Open Mirror Symmetry for Higher Dimensional Calabi-Yau Hypersurfaces

TL;DR

This paper investigates non-perturbative open-closed string corrections in higher-dimensional Calabi-Yau hypersurfaces using relative cohomology and hypergeometric systems, with explicit calculations for a fivefold example.

Contribution

It introduces a method to compute open-closed string quantum corrections for higher-dimensional Calabi-Yau manifolds using differential equations.

Findings

Derived Picard-Fuchs equations for a Calabi-Yau fivefold

Computed explicit quantum corrections in open and closed string moduli

Discussed implications for open-closed duality

Abstract

Compactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both open and closed string moduli for a class of compact Calabi-Yau manifolds in general dimensions. Our analysis is based on the methods using relative cohomology and generalized hypergeometric system. For the simplest example of compact Calabi-Yau fivefold, we explicitly derive the associated Picard-Fuchs differential equations and compute the quantum corrections in terms of the open and closed flat coordinates. Implications for a kind of open-closed duality are also discussed.