Local Models in F-Theory and M-Theory with Three Generations

We describe a general framework that can be used to geometrically engineer local, phenomenological models in F-theory and M-theory based on ALEfibrations, and we present several concrete examples of such models that feature three generations of matter with semi-realistic phenomenology. We show that the geometric structures required for generating interactions—triple-intersections of mattercurves in F-theory and supersymmetric three-cycles supporting multiple conical singularities in M-theory—are generic in such ALE-fibred manifolds, and that they can be understood in correspondence with one another. The models we can construct in this way are strictly limited in complexity by the maximality of the Ê8-ALE space, but turn out to be just complex enough to accommodate some of the most realistic string models to date. ar X iv :0 90 1. 37 85 v1 [ he pth ] 2 6 Ja n 20 09