We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N=1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a oneloop vacuum diagram. For concreteness we focus on E2-instanton effects in Type IIA vacua with intersecting D6-branes, however the same structure emerges for Type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, µ-parameter or right-handed neutrino Majorana mass terms. The latter allow the realization of the seesaw mechanism for MSSM like intersecting D-brane models.

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 ] 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 P 4 [4].

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 Uð1Þ 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 SUð5Þ grand unified theory (GUT) models this mechanism enforces a global Uð1Þ 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 Â Uð1Þ enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze F-theory GUT models.