We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC's) from the action principle. These BC's include choices that give rise to breaking of the gauge symmetries. The boundary conditions could be chosen to coincide with those commonly applied in orbifold theories, but there are many more possibilities. To investigate the nature of gauge symmetry breaking via BC's we calculate the elastic scattering amplitudes for longitudinal gauge bosons. We find that using a consistent set of BC's the terms in these amplitudes that explicitly grow with energy always cancel without having to introduce any additional scalar degree of freedom, but rather by the exchange of Kaluza-Klein (KK) gauge bosons. This suggests that perhaps the SM Higgs could be completely eliminated in favor of some KK towers of gauge fields. We show that from the low-energy effective theory perspective this seems to be indeed possible. We display an extra dimensional toy model, where BC's introduce a symmetry breaking pattern and mass spectrum that resembles that in the standard model.

The dynamics of a stabilized radion in the Randall-Sundrum model with two branes is investigated, and the effects of the radion on electroweak precision observables are evaluated. The radius is assumed to be stabilized using a bulk scalar field as suggested by Goldberger and Wise. First the mass and the wave function of the radion is determined including the back reaction of the bulk stabilization field on the metric, giving a typical radion mass of the order of the weak scale. This is demonstrated by a perturbative computation of the radion wave function. A consequence of the background configuration for the scalar field is that after including the back reaction the Kaluza-Klein states of the bulk scalars couple directly to the standard model fields on the TeV brane. Some cosmological implications are discussed, and in particular it is found that the shift in the radion at late times is in agreement with the four-dimensional effective theory result. The effect of the radion on the oblique parameters is evaluated using an effective theory approach. In the absence of a curvature-scalar Higgs mixing operator, these corrections are small and give a negative contribution to S. In the presence of such a mixing operator, however, the corrections can be sizable due to the modified Higgs and radion couplings.

We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily Anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes. We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's Law. We also comment on the possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scalar field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p + 2)-dimensions. * J. Robert Oppenheimer Fellow

We analyze the cosmology of the Randall-Sundrum model and that of compact brane models in general in the presence of a radius stabilization mechanism. We find that the expansion of our universe is generically in agreement with the expected effective four dimensional description. The constraint (which is responsible for the appearance of non-conventional cosmologies in these models) that must be imposed on the matter densities on the two branes in the theory without a stabilized radius is a consequence of requiring a static solution even in the absence of stabilization. Such constraints disappear in the presence of a stablizing potential, and the ordinary FRW (Friedmann-Robertson-Walker) equations are reproduced, with the expansion driven by the sum of the physical values of the energy densities on the two branes and in the bulk. For the case of the Randall-Sundrum model we examine the kinematics of the radion field, and find that corrections to the standard FRW equations are small for temperatures below the weak scale. We find that the radion field has renormalizable and unsuppressed couplings to Standard Model particles after electroweak symmetry breaking. These couplings may have important implications for collider searches. We comment on the possibility that matter off the TeV brane could serve as a dark matter candidate. * J. Robert Oppenheimer fellow.

We present a 5D gauge theory in warped space based on a bulk SU (2) L × SU (2) R × U (1) B−L gauge group where the gauge symmetry is broken by boundary conditions. The symmetry breaking pattern and the mass spectrum resembles that in the standard model (SM). To leading order in the warp factor the ρ parameter and the coupling of the Z (or equivalently the S-parameter) are as in the SM, while corrections are expected at the level of a percent. From the AdS/CFT point of view the model presented here can be viewed as the AdS dual of a (walking) technicolor-like theory, in the sense that it is the presence of the IR brane itself that breaks electroweak symmetry, and not a localized Higgs on the IR brane (which should be interpreted as a composite Higgs model). This model predicts the lightest W , Z and γ resonances to be at around 1.2 TeV, and no fundamental (or composite) Higgs particles.