Abelian gauge symmetries and proton decay in global<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi></mml:math>-theory GUTs

Abstract

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 ${E}_{8}$ and ${E}_{7}\ifmmode\times\else\texttimes\fi{}U(1)$ enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze $F$-theory GUT models.