Construction of mirror pairs of Berglund-Hubsch Calabi-Yau orbifolds of loop-type polynomials
Abstract
In this paper, an algorithm for constructing orbifolds of Calabi-Yau manifolds of the Berglund-Hubsch-Krawitz (BHK) type and their mirror pairs for loop-type polynomials is proposed and applied. A complete enumeration of loop polynomials satisfying the Calabi-Yau condition was carried out, yielding 216 unique polynomials. For each polynomial, the Euler characteristics, the numbers of generations and singlets were computed, and the twisted sector states were analyzed using Roan's generalized combinatorial construction. It was established that Roan pairs are absent for all studied configurations, indicating a zero contribution of the twisted sectors to the difference in Hodge numbers upon resolving the orbifold singularities. The primary physical result of this work is the discovery of two configurations with diagonal exponents {74, 3, 3, 5, 3} and {74, 3, 5, 3, 3}, for which the number of quark and lepton generations is precisely three (Ngen = 3), which is of key interest for constructing phenomenologically realistic models of particle physics.
Related
- An Algorithm for Generating All Berglund-Hubsch-Type Calabi-Yau Orbifolds and Their Mirrors. Classification of Maximal Admissible Groups
- The complete massless singlet spectrum in the free-field construction of heterotic strings on Calabi–Yau orbifolds
- Freeform Mirror Construction for a Panoramic Annular Lens Using Local Arc and Normal Control
- The one-loop QCD scale anomaly on ADE orbifolds as an index
- The Flavor of Non-Abelian Orbifolds
BibTeX
@misc{malyutin2026construction,
title = {{Construction of mirror pairs of Berglund-Hubsch Calabi-Yau orbifolds of loop-type polynomials}},
author = {Maxim Malyutin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38273},
eprint = {2609.38273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38273},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Construction of mirror pairs of Berglund-Hubsch Calabi-Yau orbifolds of loop-type polynomials
AU - Maxim Malyutin
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38273
UR - https://arxiv.org/abs/2609.38273
AB - In this paper, an algorithm for constructing orbifolds of Calabi-Yau manifolds of the Berglund-Hubsch-Krawitz (BHK) type and their mirror pairs for loop-type polynomials is proposed and applied. A complete enumeration of loop polynomials satisfying the Calabi-Yau condition was carried out, yielding 216 unique polynomials. For each polynomial, the Euler characteristics, the numbers of generations and singlets were computed, and the twisted sector states were analyzed using Roan's generalized combinatorial construction. It was established that Roan pairs are absent for all studied configurations, indicating a zero contribution of the twisted sectors to the difference in Hodge numbers upon resolving the orbifold singularities. The primary physical result of this work is the discovery of two configurations with diagonal exponents {74, 3, 3, 5, 3} and {74, 3, 5, 3, 3}, for which the number of quark and lepton generations is precisely three (N_gen = 3), which is of key interest for constructing phenomenologically realistic models of particle physics.
ER -