Consistency conditions for orientifolds and D-manifolds.

We study superstrings with orientifold projections and with generalized open string boundary conditions (D-branes). We find two types of consistency condition, one related to the algebra of Chan-Paton factors and the other to cancellation of divergences. One consequence is that the Dirichlet 5-branes of the Type I theory carry a symplectic gauge group, as required by string duality. As another application we study the Type I theory on a K3 Z2 orbifold, finding a family of consistent theories with various unitary and symplectic subgroups of U(16) × U(16). We argue that the K3 orbifold with spin connection embedded in gauge connection corresponds to an interacting conformal field theory in the Type I theory.