Equivalence of Deformations of Berglund H\"ubsch Mirror Pairs

TL;DR

This paper studies deformations of Berglund H"ubsch mirror pairs, demonstrating their equivalence in most cases through direct mapping and symmetry analysis, with detailed distinctions between 'Good' and 'Bad' models.

Contribution

It provides a comparative analysis of deformations in Berglund H"ubsch mirror pairs, establishing equivalence for a large class of models using two different methods.

Findings

Deformations are equivalent for 79 'Good' models.

Deformations differ for 77 'Bad' models.

Number and initial exponents of deformations are consistent under orbifold analysis.

Abstract

We investigate here the deformations of Berglund H\"ubsch loop and chain mirrors where the original manifolds are defined in the same weighted projective space. We show that the deformations are equivalent by two methods. First, we map directly the two models to each other and show that the deformations are the same for $79$ "Good" models, but not for the $77$ "Bad" ones. We then investigate the orbifold of the mirror pair by the maximal symmetry group and show that the number of deformations is the same and that they are almost the same, i.e., the first four exponents of the deformations are identical.