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Abstract
Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our algorithm reproduces the full set of reflexive polytopes in two and three dimensions, and in four dimensions with a small number of vertices and points. Motivated by this result, we construct five-dimensional reflexive polytopes with the lowest number of vertices and points. By calculating the normal form of the polytopes, we establish that many of these are not in existing datasets and therefore give rise to new Calabi–Yau four-folds. In some instances, the Hodge numbers we compute are new as well.
Department
Physics
Publication Date
2-6-2024
Journal Title
Physics Letters B
Publisher
Elsevier BV
Digital Object Identifier (DOI)
Document Type
Article
Recommended Citation
Per Berglund, Yang-Hui He, Elli Heyes, Edward Hirst, Vishnu Jejjala, Andre Lukas, New Calabi–Yau manifolds from genetic algorithms, Physics Letters B, Volume 850, 2024, 138504, ISSN 0370-2693, https://doi.org/10.1016/j.physletb.2024.138504.
Rights
© 2024 The Author(s).
Comments
This is an open access article published by Elsevier BV in Physics Letters B in 2024, available online: https://dx.doi.org/10.1016/j.physletb.2024.138504