Consistency conditions for orientifolds and D-manifolds

Abstract

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 five 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 $K3$ ${Z}_{2}$ orbifold, finding a family of consistent theories with various unitary and symplectic subgroups of U(16)\ifmmode\times\else\texttimes\fi{}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.