Matter from G2 manifolds

Abstract We describe how chiral matter charged under SU ( N ) and SO (2 N ) gauge groups arises from codimension seven singularities in compactifications of M-theory on manifolds with G 2 holonomy. The geometry of these spaces is that of a cone over a six-dimensional Einstein space which can be constructed by (multiple) unfolding of hyper-Kahler quotient spaces. In type IIA the corresponding picture is given by stacks of intersecting D6-branes and chiral matter arises from open strings stretching between them. Usually one obtains (bi)fundamental representations but by including orientifold six-planes in the type IIA picture we find more exotic representations like the anti-symmetric, which is important for the study of SU (5) grand unification, and trifundamental representations. We also exhibit many cases where the G 2 metrics can be described explicitly, although in general the metrics on the spaces constructed via unfolding are not known.