  We construct a solitonic 3-brane solution in the 5-dimensional
Einstein-Hilbert-Gauss-Bonnet theory. This solitonic brane is delta-function
like, and has the property that gravity is completely localized on the brane.
That is, there are no propagating degrees of freedom in the bulk, while on the
brane we have purely 4-dimensional Einstein gravity. Thus, albeit the classical
background is 5-dimensional, the quantum theory (perturbatively) is
4-dimensional. Our solution can be embedded in the supergravity context, where
we have completely localized supergravity on the corresponding solitonic brane,
which is a BPS object preserving 1/2 of the original supersymmetries. By
including a scalar field, we also construct a smooth domain wall solution,
which in a certain limit reduces to the delta-function-like solitonic brane
solution (this is possible for the latter breaks diffeomorphisms only
spontaneously). We then show that in the smooth domain wall background the only
normalizable mode is the 4-dimensional graviton zero mode, while all the other
(including massive Kaluza-Klein) modes are not even plane-wave normalizable.
Finally, we observe that in compactifications of Type IIB on 5-dimensional
Einstein manifolds other than a 5-sphere the corresponding dual gauge theories
on D3-branes are not conformal in the ultra-violet, and at the quantum level we
expect the Einstein-Hilbert term to be generated in their world-volumes. We
conjecture that in full string theory on Type IIB side this is due to higher
curvature terms, which cannot be ignored in such backgrounds. A stronger
version of this conjecture also states that (at least in some cases) in such
backgrounds D3-branes are solitonic objects with completely localized
(super)gravity in their world-volumes.
