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

Understand

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.