Branes intersecting at angles

We show that configurations of multiple D-branes related by SU(N) rotations will preserve unbroken supersymmetry. This includes cases in which two D-branes are related by a rotation of arbitrarily small angle, and we discuss some of the physics of this. In particular, we discuss a way of obtaining 4D chiral fermions on the intersection of D-branes. We also rephrase the condition for unbroken supersymmetry as the condition that a 'generalized holonomy group' associated with the brane configuration and manifold is reduced, and relate this condition (in type IIA string theory) to a condition in eleven dimensions.