Learning non-Higgsable gauge groups in 4D F-theory
We apply machine learning techniques to solve a specific classification problem in 4D F-theory. For a divisor D on a given complex threefold base, we want to read out the non-Higgsable gauge group on it using local geometric information near D. The input features are the triple intersection numbers...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2018
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| Online Access: | http://hdl.handle.net/1721.1/117358 https://orcid.org/0000-0001-7418-1519 |
| _version_ | 1811075168828653568 |
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| author | Zhang, Zhibai Wang, Yinan |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Zhang, Zhibai Wang, Yinan |
| author_sort | Zhang, Zhibai |
| collection | MIT |
| description | We apply machine learning techniques to solve a specific classification problem in 4D F-theory. For a divisor D on a given complex threefold base, we want to read out the non-Higgsable gauge group on it using local geometric information near D. The input features are the triple intersection numbers among divisors near D and the output label is the non-Higgsable gauge group. We use decision tree to solve this problem and achieved 85%-98% out-of-sample accuracies for different classes of divisors, where the data sets are generated from toric threefold bases without (4,6) curves. We have explicitly generated a large number of analytic rules directly from the decision tree and proved a small number of them. As a crosscheck, we applied these decision trees on bases with (4,6) curves as well and achieved high accuracies. Additionally, we have trained a decision tree to distinguish toric (4,6) curves as well. Finally, we present an application of these analytic rules to construct local base configurations with interesting gauge groups such as SU(3). Keywords: Differential and Algebraic Geometry, F-Theory |
| first_indexed | 2024-09-23T10:01:55Z |
| format | Article |
| id | mit-1721.1/117358 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:01:55Z |
| publishDate | 2018 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1173582022-09-26T15:17:35Z Learning non-Higgsable gauge groups in 4D F-theory Zhang, Zhibai Wang, Yinan Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Wang, Yinan We apply machine learning techniques to solve a specific classification problem in 4D F-theory. For a divisor D on a given complex threefold base, we want to read out the non-Higgsable gauge group on it using local geometric information near D. The input features are the triple intersection numbers among divisors near D and the output label is the non-Higgsable gauge group. We use decision tree to solve this problem and achieved 85%-98% out-of-sample accuracies for different classes of divisors, where the data sets are generated from toric threefold bases without (4,6) curves. We have explicitly generated a large number of analytic rules directly from the decision tree and proved a small number of them. As a crosscheck, we applied these decision trees on bases with (4,6) curves as well and achieved high accuracies. Additionally, we have trained a decision tree to distinguish toric (4,6) curves as well. Finally, we present an application of these analytic rules to construct local base configurations with interesting gauge groups such as SU(3). Keywords: Differential and Algebraic Geometry, F-Theory United States. Department of Energy (Contract DE-SC00012567) 2018-08-14T17:23:27Z 2018-08-14T17:23:27Z 2018-08 2018-07 2018-08-05T03:56:12Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 http://hdl.handle.net/1721.1/117358 Wang, Yi-Nan, and Zhibai Zhang. “Learning Non-Higgsable Gauge Groups in 4D F-Theory.” Journal of High Energy Physics, vol. 2018, no. 8, Aug. 2018. © The Authors https://orcid.org/0000-0001-7418-1519 en https://doi.org/10.1007/JHEP08(2018)009 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 | Zhang, Zhibai Wang, Yinan Learning non-Higgsable gauge groups in 4D F-theory |
| title | Learning non-Higgsable gauge groups in 4D F-theory |
| title_full | Learning non-Higgsable gauge groups in 4D F-theory |
| title_fullStr | Learning non-Higgsable gauge groups in 4D F-theory |
| title_full_unstemmed | Learning non-Higgsable gauge groups in 4D F-theory |
| title_short | Learning non-Higgsable gauge groups in 4D F-theory |
| title_sort | learning non higgsable gauge groups in 4d f theory |
| url | http://hdl.handle.net/1721.1/117358 https://orcid.org/0000-0001-7418-1519 |
| work_keys_str_mv | AT zhangzhibai learningnonhiggsablegaugegroupsin4dftheory AT wangyinan learningnonhiggsablegaugegroupsin4dftheory |