Supersymmetric Three Family SU(5) Grand Unified Models from Type IIA Orientifolds with Intersecting D6-Branes

We construct some N = 1 supersymmetric three-family SU(5) Grand Unified Models from type IIA orientifolds on T6/(Z2 × Z2) with D6-branes intersecting at general angles. These constructions are supersymmetric only for special choices of untwisted moduli. We show that within the above class of constructions there are no supersymmetric three-family models with 3 copies of 10-plets unless there are simultaneously some 15-plets. We systematically analyze the construction of such models and their spectra. The M-theory lifts of these brane constructions become purely geometrical backgrounds: they are singular G2 manifolds where the Grand Unified gauge symmetries and three families of chiral fermions are localized at codimension 4 and codimension 7 singularities respectively. We also study some preliminary phenomenological features of the models.