Gravitational Higgs Mechanism

We discuss the gravitational Higgs mechanism in domain wall background solutions that arise in the theory of 5-dimensional Einstein-Hilbert gravity coupled to a scalar field with a non-trivial potential. The scalar fluctuations in such backgrounds can be completely gauged away, and so can be the graviphoton fluctuations. On the other hand, we show that the graviscalar fluctuations do not have normalizable modes. As to the 4-dimensional graviton fluctuations, in the case where the volume of the transverse dimension is finite the massive modes are plane-wave normalizable, while the zero mode is quadratically normalizable. We then discuss the coupling of domain wall gravity to localized 4-dimensional matter. In particular, we point out that this coupling is consistent only if the matter is conformal. This is different from the Randall-Sundrum case as there is a discontinuity in the delta-function-like limit of such a smooth domain wall - the latter breaks diffeomorphisms only spontaneously, while the Randall-Sundrum brane breaks diffeomorphisms explicitly. Finally, at the quantum level both the domain wall as well as the Randall-Sundrum setups suffer from inconsistencies in the coupling between gravity and localized matter, as well as the fact that gravity is generically expected to be delocalized in such backgrounds due to higher curvature terms.Comment: 16 pages, revtex; a minor correctio

"Self-tuning" and Conformality

We consider an infinite-volume brane world setup where a codimension one brane is coupled to bulk gravity plus a scalar field with vanishing potential. The latter is protected by bulk supersymmetry, which is intact even if brane supersymmetry is completely broken as the volume of the extra dimension is infinite. Within this setup we discuss a flat solution with a ``self-tuning'' property, that is, such a solution exists for a continuous range of values for the brane tension. This infinite-volume solution is free of any singularities, and has the property that the brane cosmological constant is protected by bulk supersymmetry. We, however, also point out that consistency of the coupling between bulk gravity and brane matter generically appears to require that the brane world-volume theory be conformal.Comment: 13 pages, revtex; minor misprints and references corrected, clarifying remarks added (to appear in Mod. Phys. Lett. A

A Remark on Non-conformal Non-supersymmetric Theories with Vanishing Vacuum Energy Density

We discuss non-conformal non-supersymmetric large N gauge theories with vanishing vacuum energy density to all orders in perturbation theory. These gauge theories can be obtained via a field theory limit of Type IIB D3-branes embedded in orbifolded space-times. We also discuss gravity in this setup.Comment: 13 pages, revtex; a minor change in wordin

Solitonic Brane World with Completely Localized (Super)Gravity

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.Comment: 28 pages, revtex; a reference and clarifying remarks adde