TY - JOUR
T1 - Open virtual structure constants and mirror computation of open gromov-witten invariants of projective hypersurfaces
AU - Jinzenji, Masao
AU - Shimizu, Masahide
N1 - Funding Information:
M. Jinzenji would like to thank Miruko Jinzenji for kind encouragement. M. Shimizu would like to thank Dr. Yutaka Tobita for assistance of numerical computations using Mathematica. Research of M. Jinzenji is partially supported by JSPS Grant No. 22540061.
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
KW - Mirror symmetry
KW - open Gromov-Witten invariants
KW - projective hypersurface
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U2 - 10.1142/S0219887814500054
DO - 10.1142/S0219887814500054
M3 - Article
AN - SCOPUS:84891032137
SN - 0219-8878
VL - 11
JO - International Journal of Geometric Methods in Modern Physics
JF - International Journal of Geometric Methods in Modern Physics
IS - 1
M1 - 1450005
ER -