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

TL;DR

This paper employs machine learning, specifically decision trees, to classify non-Higgsable gauge groups in 4D F-theory based on local geometric data, achieving high accuracy and deriving explicit analytic rules.

Contribution

It introduces a machine learning approach to classify gauge groups in 4D F-theory and derives explicit analytic rules from decision trees, enhancing understanding of geometric classification.

Findings

Achieved 85%-98% accuracy in classifying gauge groups.

Generated and proved explicit analytic rules from decision trees.

Successfully applied rules to bases with (4,6) curves and constructed local base configurations.

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).