Construction of mirror pairs Calabi-Yau orbifolds of the Berglund-Hubsch type

TL;DR

This paper presents an algorithm to systematically identify mirror pairs of Berglund-Hubsch-type Calabi-Yau orbifolds, including their deformations and particle content, advancing understanding of mirror symmetry in string theory.

Contribution

The authors developed a general algorithm for constructing all mirror pairs of Berglund-Hubsch-type Calabi-Yau orbifolds and their deformations.

Findings

Successfully identified all mirror pairs for a Fermat-type Calabi-Yau model.

Determined the number of generations and singlets for each mirror pair.

Provided explicit data on particle content in the constructed orbifolds.

Abstract

In this paper we have developed general algorithm for finding all orbifolds of Berglund-Hubsch-type Calabi-Yau manifolds and their mirrors. An explicit construction is formulated for finding all admissible deformations and groups defining mirror pairs of orbifolds. Then using our algorithm for one of the Calabi-Yau manifolds, defined by a Fermat-type polynomial, we found all mirror pairs of orbifolds. For this model, for each pair of orbifolds, the number of generations and the number of singlets i.e. particles participating only in gravitational interactions (dark matter particles) were found.