$\mathbb{P}^1$-bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models

TL;DR

This paper investigates a large class of 4D F-theory models from $P^1$-bundle bases, revealing that non-Higgsable gauge groups are prevalent, with many models supporting realistic gauge structures and potential dark matter candidates.

Contribution

It demonstrates that non-Higgsable gauge groups are widespread in 4D F-theory compactifications on $P^1$-bundle bases, providing new insights into their geometric and physical properties.

Findings

98.3% of studied bases have non-Higgsable gauge factors.

Many bases support $SU(3) imes SU(2)$ clusters relevant for phenomenology.

Only 80 out of 100,000 bases are weak Fano with no automatic singularities.

Abstract

We explore a large class of F-theory compactifications to four dimensions. We find evidence that gauge groups that cannot be Higgsed without breaking supersymmetry, often accompanied by associated matter fields, are a ubiquitous feature in the landscape of ${\cal N} = 1$ 4D F-theory constructions. In particular, we study 4D F-theory models that arise from compactification on threefold bases that are $\mathbb{P}^1$ bundles over certain toric surfaces. These bases are one natural analogue to the minimal models for base surfaces for 6D F-theory compactifications. Of the roughly 100,000 bases that we study, only 80 are weak Fano bases in which there are no automatic singularities on the associated elliptic Calabi-Yau fourfolds, and 98.3% of the bases have geometrically non-Higgsable gauge factors. The $\mathbb{P}^1$-bundle threefold bases we analyze contain a wide range of distinct surface topologies that support geometrically non-Higgsable clusters. Many of the bases that we consider contain $SU(3)\times SU(2)$ seven-brane clusters for generic values of deformation moduli; we analyze the relative frequency of this combination relative to the other four possible two-factor non-Higgsable product groups, as well as various other features such as geometrically non-Higgsable candidates for dark matter structure and phenomenological ($SU(2)$-charged) Higgs fields.