  We discuss the low energy effective action for the Bosonic and Fermionic
zero-modes of a smooth BPS Randall-Sundrum domain wall, including the induced
supergravity on the wall. The result is a pure supergravity in one lower
dimension. In particular, and in contrast to non-gravitational domain walls or
domain walls in a compact space, the zero-modes representing transverse
fluctuations of domain wall have vanishing action.
