Spacetime-Filling Branes in Ten and Nine Dimensions

Type-IIB supergravity in ten dimensions admits two consistent $Z_2$ truncations. After the insertion of D9-branes, one of them leads to the low-energy action of type-I string theory, and it can be performed in two different ways, in correspondence with the fact that there are two different consistent ten-dimensional type-I string theories, namely the SO(32) superstring and the $USp(32)$ model, in which supersymmetry is broken on the D9-branes. We derive here the same results for Type-IIA theory compactified on a circle in the presence of D8-branes. We also analyze the $\kappa$-symmetric action for a brane charged with respect to the S-dual of the RR 10-form of type-IIB, and we find that the tension of such an object has to scale like $g_S^{-2}$ in the string frame. We give an argument to explain why this result is in disagreement with the one obtained using Weyl rescaling of the brane action, and we argue that this brane can only be consistently introduced if the other $Z_2$ truncation of type-IIB is performed. Moreover, we find that one can include a 10-form in type-IIA supersymmetry algebra, and also in this case the corresponding $\kappa$-symmetric brane has a tension scaling like $g_S^{-2}$ in the string frame.