## Abstract

We consider an (N - 2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of the Fermat type) in CP^{N-1} and its mirror manifold. We introduce an (N -2)-point correlation function (generalized Yukawa coupling) and evaluate it both by solving the Picard-Fuchs equation for period integrals in the mirror manifold and by explicitly calculating the contribution of holomorphic maps of degree 1 to the Yukawa coupling in the Calabi-Yau manifold using the method of algebraic geometry. In enumerating the holomorphic curves in the general-dimensional Calabi-Yau manifolds, we extend the method of counting rational curves on the Calabi-Yau three-fold using the Shubert calculus on Gr(2, N). The agreement of the two calculations for the (N - 2)-point function establishes "the mirror symmetry at the correlation function level" in the general-dimensional case.

Original language | English |
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Pages (from-to) | 1217-1252 |

Number of pages | 36 |

Journal | International Journal of Modern Physics A |

Volume | 11 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1996 |

Externally published | Yes |

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics