Gravitational Couplings, Orientifolds and M-Planes

We examine string-theory orientifold planes of various types including the Sp and SO-odd planes, and deduce the gravitational Chern-Simons couplings on their world-volumes. Consistency checks are carried out in different spacetime dimensions using various dualities, including those relating string theory with F-theory and M-theory. It is shown that when an orientifold 3-plane crosses a 5-brane, the jump in the charge is accompanied by a corresponding change in the gravitational couplings.