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).