Mirror Symmetry and An Exact Calculation of N-2 Point Correlation Function on Calabi-Yau Manifold embedded in CP^{N-1}

TL;DR

This paper computes the (N-2)-point correlation function on a class of Calabi-Yau manifolds embedded in projective space, using mirror symmetry and algebraic geometry techniques for exact results.

Contribution

It provides an exact calculation of the N-2 point correlation function on specific Calabi-Yau manifolds via mirror symmetry and algebraic geometry methods.

Findings

Explicit formula for the correlation function derived

Validation of mirror symmetry through exact calculations

Method applicable to other Calabi-Yau manifolds

Abstract

We consider an (N-2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of Fermat type) in CP^{N-1} and its mirror manifold. We introduce the (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 also 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...