It was recently pointed out by E. Witten that for a D-brane to consistently wrap a submanifold of some manifold, the normal bundle must admit a Spin c structure. We examine this constraint in the case of type II string compactifications with vanishing cosmological constant, and argue that in all such cases, the normal bundle to a supersymmetric cycle is automatically Spin

Let R be a regular ring, essentially of finite type over a perfect field k. An R–module M is called a unit R[F ]–module if it comes equipped with an isomorphism F M −→ M, where F denotes the Frobenius map on SpecR, and F e∗ is the associated pullback functor. It is well known that M then carries a natural DR–module structure. In this paper we investigate the relation between the unit R[F ]–stru...