The Global Gauge Group Structure of F-theory Compactification with U(1)s
Mirjam Cvetic, Ling Lin
TL;DR
The work shows that F-theory compactifications with abelian factors intrinsically carry a non-trivial global gauge group structure due to the Shioda map of Mordell--Weil generators, leading to refined charge quantization and central quotients $G_{\text{glob}}=(U(1)\times\tilde{G})/{\mathbb{Z}}_{\kappa}$. It provides explicit constructions, including SM-like realizations with $[SU(3)\times SU(2)\times U(1)]/\mathbb{Z}_6$, and analyzes how different Mordell--Weil ranks or torsion modify the centre and allowed representations. The paper also shows how higgsing/unhiggsing along specific fibre splits reproduces or constrains the observed global structure and discusses a swampland criterion grounded in the geometrically preferred U(1) charge normalization, suggesting that singlet charges fix the charge lattice and distinguish EFTs that can arise from F-theory. Together, these results illuminate the geometric origin of global gauge structures, guide phenomenological model building, and connect to broader quantum gravity constraints. The findings have implications for Standard Model embeddings, model building with multiple U(1)s, and potential links to the weak gravity conjecture and related swampland ideas.
Abstract
We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell--Weil generators. This results in constraints on the U(1) charges of non-abelian matter consistent with observations made throughout the literature. In particular, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU(3)xSU(2)xU(1)]/Z6. Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an SU(2)xU(1) gauge theory can either unhiggs into an SU(2)xSU(2) or an SU(3)xSU(2) theory. We also study implications of the charge constraints as a criterion for the F-theory 'swampland'.