Gravitational Duality , Branes and Charges

It is argued that D = 10 type II strings and M-theory in D = 11 have D − 5 branes and 9-branes that are not standard p-branes coupled to anti-symmetric tensors. The global charges in a D-dimensional theory of gravity consist of a momentum P M and a dual D − 5 form charge K M1...MD−5 , which is related to the NUT charge. On dimensional reduction, P gives the electric charge and K the magnetic charge of the graviphoton. The charge K is constructed and shown to occur in the superalgebra and BPS bounds in D ≥ 5, and leads to a NUT-charge modification of the BPS bound in D = 4. K is carried by Kaluza-Klein monopoles, which can be regarded as D − 5 branes. Supersymmetry and U-duality imply that the type IIB theory has (p, q) 9-branes. Orientifolding with 32 (0,1) 9-branes gives the type I string, while modding out by a related discrete symmetry with 32 (1,0) 9-branes gives the SO(32) heterotic string. Symmetry enhancement, the effective world-volume theories and the possibility of a twelve dimensional origin are discussed.