Global F-theory GUTs

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi–Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S[U(4)×U(1)X]S[U(4)×U(1)X] spectral cover, which allows for the phenomenologically relevant Yukawa couplings and GUT breaking to the MSSM via hypercharge flux while preventing dimension-4 proton decay. General expressions for the massless spectrum, consistency conditions and a new method for the computation of curvature-induced tadpoles are presented. We also provide a geometric toolkit for further model searches in the framework of toric geometry. Finally, an explicit global model with three chiral generations and all required Yukawa couplings is defined on a Calabi–Yau fourfold which is fibered over the del Pezzo transition of the Fano threefold P4[4]P4[4].