In this paper, we generalize Walcher's computation of the open Gromov-Witten invariants of the quintic hypersurface to Fano and Calabi-Yau projective hypersurfaces. Our main tool is the open virtual structure constants. We also propose the generalized mirror transformation for the open Gromov-Witten invariants, some parts of which are proven explicitly. We also discuss possible modification of the multiple covering formula for the case of higher-dimensional Calabi-Yau manifolds. The generalized disk invariants for some Calabi-Yau and Fano manifolds are shown and they are certainly integers after resummation by the modified multiple covering formula. This paper also contains the direct integration method of the period integrals for higher-dimensional Calabi-Yau hypersurfaces in the Appendix.
|Journal||International Journal of Geometric Methods in Modern Physics|
|Publication status||Published - Jan 2014|
- Mirror symmetry
- open Gromov-Witten invariants
- projective hypersurface
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)