On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs

TL;DR

Grimm and Weigand address the global emergence of abelian gauge symmetries in four-dimensional F-theory GUTs, showing that global Tate-model restrictions can guarantee un-higgsed $U(1)_X$ factors and forbid dimension-4 proton decay. By resolving singular Calabi–Yau fourfolds and examining the Coulomb branch, they connect abelian data to an underlying $E_8$ structure and its decompositions, while identifying a global mechanism via an extended Dynkin node that yields massive $U(1)$s or massless abelian factors depending on the deformation. They further relate these global geometric features to brane recombination in orientifolds and to mirror-symmetric duals, using mirror symmetry to map spectral-cover data to dual gauge factors and test the global validity of spectral-cover constructions. The work highlights a global, geometry-driven route to engineer abelian selection rules in F-theory GUTs, elucidates implications for right-handed neutrinos and proton stability, and notes significant D3-tadpole constraints arising from the $U(1)$ restriction, guiding future flux and moduli analyses.

Abstract

The existence of abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau fourfold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) GUT models this mechanism enforces a global U(1)_X symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau fourfolds and their mirror duals starting from an underlying E_8 and E_7 x U(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyse F-theory GUT models.