Branes on the Brane

We show that four-dimensional N = 2 ungauged Einstein-Maxwell supergravity can be embedded on the Randall-Sundrum 3-brane, as a consistent Kaluza-Klein reduction of five-dimensional N = 4 gauged supergravity. In particular, this allows us to describe four-dimensional Reissner-Nordström black holes within the Randall-Sundrum scenario. Using earlier results on the embedding of five-dimensional N = 4 gauged supergravity in ten dimensions, we can then describe the four-dimensional Einstein-Maxwell supergravity on the 3-brane, and its solutions, from a type IIB viewpoint. We also show that the minimal ungauged supergravities in D = 5 and D = 6 can be consistently embedded in the half-maximally supersymmetric gauged supergravities in D = 6 and D = 7 respectively. These allow us to construct solutions including BPS black holes and strings living in " Randall-Sundrum 4-branes, " and BPS self-dual strings living in " Randall-Sundrum 5-branes. " We can also lift the embeddings to ten-dimensional massive type IIA and D = 11 supergravity respectively. In particular, we obtain a solution describing the self-dual string living in the world-volume of an M5-brane, which can be viewed as an open membrane ending on the M5-brane.