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Title: Learning non-Higgsable gauge groups in 4D F-theory

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).

Authors:
 [1];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics, Dept. of Physics
  2. New York Univ. (NYU), NY (United States). Tandon School of Engineering, Dept. of Finance and Risk Engineering
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1505580
Grant/Contract Number:  
[SC0012567]
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
[Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 8]; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Differential and Algebraic Geometry; F-Theory

Citation Formats

Wang, Yi-Nan, and Zhang, Zhibai. Learning non-Higgsable gauge groups in 4D F-theory. United States: N. p., 2018. Web. doi:10.1007/jhep08(2018)009.
Wang, Yi-Nan, & Zhang, Zhibai. Learning non-Higgsable gauge groups in 4D F-theory. United States. doi:10.1007/jhep08(2018)009.
Wang, Yi-Nan, and Zhang, Zhibai. Fri . "Learning non-Higgsable gauge groups in 4D F-theory". United States. doi:10.1007/jhep08(2018)009. https://www.osti.gov/servlets/purl/1505580.
@article{osti_1505580,
title = {Learning non-Higgsable gauge groups in 4D F-theory},
author = {Wang, Yi-Nan and Zhang, Zhibai},
abstractNote = {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).},
doi = {10.1007/jhep08(2018)009},
journal = {Journal of High Energy Physics (Online)},
number = [8],
volume = [2018],
place = {United States},
year = {2018},
month = {8}
}

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Cited by: 7 works
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