Worldvolume Dynamics of D-branes in a D-brane Background

We study the embedding of D(8-p)-branes in the background geometry of parallel Dp-branes for $p\le 6$. The D(8-p)-brane is extended along the directions orthogonal to the Dp-branes of the background. The D(8-p)-brane configuration is determined by its Dirac-Born-Infeld plus Wess-Zumino-Witten action. We find a BPS condition which solves the equation of motion. The analytical solution of the BPS equation for the near-horizon and asymptotically flat geometries is given. The embeddings we obtain represent branes joined by tubes. By analyzing the energy of these tubes we conclude that they can be regarded as bundles of fundamental strings. Our solution provides an explicit realization of the Hanany-Witten effect. When $p=6$ the solution of the BPS equation must be considered separately and, in general, the embeddings of the D2-branes do not admit the same interpretation as in the $p<6$ case.