Solitonic brane world with completely localized (super)gravity

We construct a solitonic three-brane solution in the five-dimensional Einst ein-Hilbert-Gauss-Bonnet theory. This solitonic brane is delta -function-li ke, 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 four-dimensional Einstein gravity. Thus, albeit t he classical background is five-dimensional, the quantum theory (perturbati vely) is four-dimensional. Our solution can be embedded in the supergravity context, where we have completely localized supergravity on the correspond ing solitonic brane, which is a BPS object preserving 1/2 of the original s upersymmetries. By including a scalar field, we also construct a smooth dom ain wail solution, which in a certain limit reduces to the delta -function- like solitonic brane solution (this is possible for the latter breaks diffe omorphisms only spontaneously). We then show that in the smooth domain wall background the only normalizable mode is the four-dimensional graviton zer o 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 five-dimensional Einstein manifolds other than a five-spher e the corresponding dual gauge theories on D3-branes are not conformal in t he ultraviolet, and at the quantum level we expect the Einstein-Hilbert ter m 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 canno t be ignored in such backgrounds. A stronger version of this conjecture als o states that (at least in some cases) in such backgrounds D3-branes are so litonic objects with completely localized (super)gravity in their world vol umes.