Brane transfer operations and T-duality of non-BPS states

Using the relation between D-brane charges and K-theory, we study non-BPS D -branes and their behavior under T-duality. We point out that in general co mpactifications, D-brane charges are classified by relative K-theory groups . T-duality is found to act as a symmetry between the relative K-theory gro ups in Type II and Type I/IA theories. We also study Type (IA) over tilde t heory (which contains an O8(-) plane and an O8(+) plane), using K-theory an d T-duality to identify its stable D-branes. Comparison with string theory constructions reveals two interesting effects. One of them involves the tra nsfer of branes between O-planes, while in the other, a D-brane charge whic h seems conserved near one O-plane in fact decays due to the presence of an other type of O-plane.