Conformal brane world and cosmological constant

We consider a recently proposed setup where a codimension one brane is embe dded in the background of a smooth domain wall interpolating between AdS an d Minkowski minima. Since the volume of the transverse dimension is infinit e, bulk supersymmetry is intact even if brane supersymmetry is completely b roken. On the other hand, in this setup unbroken bulk supersymmetry is inco mpatible with non-zero brane cosmological constant, so the former appears t o protect the latter. In this paper we point out that, to have a consistent coupling between matter localized on the brane and bulk gravity, in this s etup generically it appears to be necessary that the brane world-volume the ory be conformal. Thus, unbroken bulk supersymmetry appears to actually pro tect not only the cosmological constant but also conformal invariance on th e brane. (C) 2000 Elsevier Science B.V. All rights reserved.