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

• Published in: The journal of high energy physics Vol. 2018; no. 8; pp. 1 - 50
• Main Authors: Wang, Yi-Nan, Zhang, Zhibai
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Decision analysis; Decision trees; Differential and Algebraic Geometry; Elementary Particles; F-Theory; High energy physics; Machine learning; MATHEMATICS AND COMPUTING; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; F-Theory; Differential and Algebraic Geometry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2018)009

A bstract 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).