Non-Higgsable clusters for 4D F-theory models

TL;DR

This paper investigates the geometric origins of non-Higgsable clusters in 4D F-theory models, revealing their role in naturally producing parts of the standard model gauge group and potential dark matter structures.

Contribution

It identifies the possible gauge group configurations and matter content arising from non-Higgsable clusters in 4D F-theory compactifications, including new complex arrangements.

Findings

Nine distinct single nonabelian gauge groups identified.

Five types of two-factor gauge group products with matter.

Complex configurations with multiple gauge factors and matter interactions.

Abstract

We analyze non-Higgsable clusters of gauge groups and matter that can arise at the level of geometry in 4D F-theory models. Non-Higgsable clusters seem to be generic features of F-theory compactifications, and give rise naturally to structures that include the nonabelian part of the standard model gauge group and certain specific types of potential dark matter candidates. In particular, there are nine distinct single nonabelian gauge group factors, and only five distinct products of two nonabelian gauge group factors with matter, including $SU(3) \times SU(2)$, that can be realized through 4D non-Higgsable clusters. There are also more complicated configurations involving more than two gauge factors; in particular, the collection of gauge group factors with jointly charged matter can exhibit branchings, loops, and long linear chains.