Abelian gauge symmetries and proton decay in globalF-theory GUTs

The existence of Abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold 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 $SU(5)$ grand unified theory (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 four-folds and their mirror duals starting from an underlying E₈ and E₇×U(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze F-theory GUT models.