Efficient Algorithm for Generating Homotopy Inequivalent Calabi-Yaus
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911560881930240 |
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| author | MacFadden, Nate |
| author_facet | MacFadden, Nate |
| contents | We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke database is foreseeably impossible due to the large count of distinct FRSTs. Moreover, such an enumeration is needlessly redundant because many such triangulations have the same restrictions to 2-faces and hence, by Wall's theorem, lead to equivalent Calabi-Yau threefolds. We show that this redundancy can be circumvented by finding a height vector in the strict interior of the intersection of the secondary cones associated with each 2-face triangulation. We demonstrate that such triangulations are generated with orders of magnitude fewer operations than the naive approach of generating all FRSTs and selecting only those differing on 2-faces. Similar methods are also presented to directly generate (the support of) the secondary subfan of all fine triangulations, relevant for random sampling of FRSTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10855 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient Algorithm for Generating Homotopy Inequivalent Calabi-Yaus MacFadden, Nate High Energy Physics - Theory Computational Physics We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke database is foreseeably impossible due to the large count of distinct FRSTs. Moreover, such an enumeration is needlessly redundant because many such triangulations have the same restrictions to 2-faces and hence, by Wall's theorem, lead to equivalent Calabi-Yau threefolds. We show that this redundancy can be circumvented by finding a height vector in the strict interior of the intersection of the secondary cones associated with each 2-face triangulation. We demonstrate that such triangulations are generated with orders of magnitude fewer operations than the naive approach of generating all FRSTs and selecting only those differing on 2-faces. Similar methods are also presented to directly generate (the support of) the secondary subfan of all fine triangulations, relevant for random sampling of FRSTs. |
| title | Efficient Algorithm for Generating Homotopy Inequivalent Calabi-Yaus |
| topic | High Energy Physics - Theory Computational Physics |
| url | https://arxiv.org/abs/2309.10855 |