Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

Abstract

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 CalabiYau 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.

On the flux vacua in F-theory compactifications

“…= ( 0, −2, 1, 0, 1, 0, 0, 1, −1, 0), 2 = (−6, 1, 0, 0, 0, 2, 3, 0, 0, 0), 3 = ( 0, −1, 0, 1, 0, 0, 0, −1, 1, 0), 4 = ( 0, −1, 0, −1, 0, 0, 0, 1, 0, 1). (3.1)1 Here we would like to comment that we have also evaluated another simple Calabi-Yau fourfold studied in[20,21] and confirmed that there are no desirable perturbative solutions with flat directions, largely because in that case the tadpole cancellation condition becomes too severe.2 See[14][15][16][17][18] for the details about explicit constructions of the background based on mirror symmetry techniques.…”