Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

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.