Mirror Symmetry on Arbitrary Dimensional Calabi-Yau Manifold with a few moduli

TL;DR

This paper extends mirror symmetry calculations to higher-dimensional Calabi-Yau manifolds with multiple moduli using toric geometry, focusing on a specific family with two marginal operators.

Contribution

It generalizes previous work on one-moduli Calabi-Yau manifolds to cases with multiple moduli, providing new computational methods via toric geometry.

Findings

Calculated the B-model on the mirror pair of specific higher-dimensional Calabi-Yau manifolds.

Extended mirror symmetry techniques to manifolds with multiple moduli.

Demonstrated the applicability of toric geometry in complex moduli space analysis.

Abstract

We calculate the B-model on the mirror pair of $X_{2N-2}(2,2,\cdots,2,1,1)$ , which is an $(N-2)$-dimensional Calabi-Yau manifold and has two marginal operators i.e. $h^{1,1}(X_{2N-2}(2,2,\cdots,2,1,1))=2$. In \cite{nagandjin} we have discussed about mirror symmetry on $X_N(1,1,\cdots,1)$ and its mirror pair. However, $X_N(1,1,\cdots,1)$ had only one moduli. In this paper we extend its methods to the case with a few moduli using toric geometry.