Scanning the skeleton of the 4D F-theory landscape
Using a one-way Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in four-dimensional F-theory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2018
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| Online Access: | http://hdl.handle.net/1721.1/115054 https://orcid.org/0000-0001-8566-6706 https://orcid.org/0000-0001-7418-1519 |
| _version_ | 1826199585357299712 |
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| author | Taylor IV, Washington Wang, Yinan |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Taylor IV, Washington Wang, Yinan |
| author_sort | Taylor IV, Washington |
| collection | MIT |
| description | Using a one-way Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in four-dimensional F-theory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials (f, g) can vanish to order (4, 6) or higher on codimension-two loci and the “good” bases where these (4, 6) loci are not allowed. A simple estimate suggests that the number of distinct resolvable base geometries exceeds 103000, with over 10250 “good” bases, though the actual numbers are likely much larger. We find that the good bases are concentrated at specific “end points” with special isolated values of h1,1 that are bigger than 1,000. These end point bases give Calabi-Yau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The non-Higgsable gauge groups on the end point bases are almost entirely made of products of E8, F4, G2 and SU(2). Nonetheless, we find a large class of good bases with a single non-Higgsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h1,1(B) ∼ 50-200 that cannot be contracted to another smooth threefold base. Keywords: Differential and Algebraic Geometry; F-Theory; Superstring Vacua |
| first_indexed | 2024-09-23T11:22:18Z |
| format | Article |
| id | mit-1721.1/115054 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:22:18Z |
| publishDate | 2018 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1150542022-10-01T03:11:20Z Scanning the skeleton of the 4D F-theory landscape Taylor IV, Washington Wang, Yinan Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Taylor IV, Washington Wang, Yinan Using a one-way Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in four-dimensional F-theory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials (f, g) can vanish to order (4, 6) or higher on codimension-two loci and the “good” bases where these (4, 6) loci are not allowed. A simple estimate suggests that the number of distinct resolvable base geometries exceeds 103000, with over 10250 “good” bases, though the actual numbers are likely much larger. We find that the good bases are concentrated at specific “end points” with special isolated values of h1,1 that are bigger than 1,000. These end point bases give Calabi-Yau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The non-Higgsable gauge groups on the end point bases are almost entirely made of products of E8, F4, G2 and SU(2). Nonetheless, we find a large class of good bases with a single non-Higgsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h1,1(B) ∼ 50-200 that cannot be contracted to another smooth threefold base. Keywords: Differential and Algebraic Geometry; F-Theory; Superstring Vacua United States. Department of Energy (Contract DE-SC00012567) 2018-04-27T18:45:17Z 2018-04-27T18:45:17Z 2018-01 2017-11 2018-01-25T10:35:09Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 http://hdl.handle.net/1721.1/115054 Taylor, Washington and Yi-Nan Wang. "Scanning the skeleton of the 4D F-theory landscape." Journal of High Energy Physics 2018 (January 2018): 111 © 2018 The Authors https://orcid.org/0000-0001-8566-6706 https://orcid.org/0000-0001-7418-1519 en http://dx.doi.org/10.1007/JHEP01(2018)111 Journal of High Energy Physics Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Taylor IV, Washington Wang, Yinan Scanning the skeleton of the 4D F-theory landscape |
| title | Scanning the skeleton of the 4D F-theory landscape |
| title_full | Scanning the skeleton of the 4D F-theory landscape |
| title_fullStr | Scanning the skeleton of the 4D F-theory landscape |
| title_full_unstemmed | Scanning the skeleton of the 4D F-theory landscape |
| title_short | Scanning the skeleton of the 4D F-theory landscape |
| title_sort | scanning the skeleton of the 4d f theory landscape |
| url | http://hdl.handle.net/1721.1/115054 https://orcid.org/0000-0001-8566-6706 https://orcid.org/0000-0001-7418-1519 |
| work_keys_str_mv | AT taylorivwashington scanningtheskeletonofthe4dftheorylandscape AT wangyinan scanningtheskeletonofthe4dftheorylandscape |