Effective supergravity for supergravity domain walls

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.