Generalized N=1 and N=2 structures in M-theory and type II orientifolds

We consider M-theory and type IIA reductions to four dimensions with N = 2 and N = 1 supersymmetry and discuss their interconnection. Our work is based on the framework of Exceptional Generalized Geometry (EGG), which extends the tangent bundle to include all symmetries in M-theory and type II string theory, covariantizing the local U-duality group E-7(7). We describe general N = 1 and N = 2 reductions in terms of SU(7) and SU(6) structures on this bundle and thereby derive the effective four-dimensional N = 1 and N = 2 couplings, in particular we compute the Kahler and hyper-Kahler potentials as well as the triplet of Killing prepotentials (or the superpotential in the N = 1 case). These structures and couplings can be described in terms of forms on an eight-dimensional tangent space where SL(8) subset of E-7 acts, which might indicate a description in terms of an eight-dimensional internal space, similar to F-theory. We finally discuss an orbifold action in M-theory and its reduction to O6 orientifolds, and show how the projection on the N = 2 structures selects the N = 1 ones. We briefly comment on new orientifold projections, U-dual to the standard ones.