Learning non-Higgsable gauge groups in 4D F-theory
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13130_2018_Article_8731.pdf
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Author(s)
Zhang, Zhibai
Wang, Yinan
Date Issued
August 2018
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
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.
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Version
Final published version
Abstract
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
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP08(2018)009
