Noncompact Extra Dimension Research Articles

Relativistic stars in Randall-Sundrum gravity

The non-linear behaviour of Randall-Sundrum gravity with one brane is examined. Due to the non-compact extra dimension, the perturbation spectrum has no mass gap, and the long wavelength effective theory is only understood perturbatively. The full 5-dimensional Einstein equations are solved numerically for static, spherically symmetric matter localized on the brane, yielding regular geometries in the bulk with axial symmetry. An elliptic relaxation method is used, allowing both the brane and asymptotic radiation boundary conditions to be simultaneously imposed. The same data that specifies stars in 4-dimensional gravity, uniquely constructs a 5-dimensional solution. The algorithm performs best for small stars (radius less than the AdS length) yielding highly non-linear solutions. An upper mass limit is observed for these small stars, and the geometry shows no global pathologies. The geometric perturbation is shown to remain localized near the brane at high densities, the confinement interestingly increasing for both small and large stars as the upper mass limit is approached. Furthermore, the static spatial sections are found to be approximately conformal to those of AdS. We show that the intrinsic geometry of large stars, with radius several times the AdS length, is described by 4-dimensional General Relativity far past the perturbative regime. This indicates that the non-linear long wavelength effective action remains local, even though the perturbation spectrum has no mass gap. The implication is that Randall-Sundrum gravity, with localized brane matter, reproduces relativistic astrophysical solutions, such as neutron stars and massive black holes, consistent with observation.

Experimental probes of the Randall-Sundrum infinite extra dimension

The phenomenological possibilities of the Randall-Sundrum non-compact extra dimension scenario with the AdS horizon increased to approximately a millimeter length, corresponding to an effective brane tension of TeV^4, are investigated. The corrections to the Newtonian potential are found to be the only observationally accessible probe of this scenario, as previously suggested in the literature. In particular, the presence of the continuum of KK modes does not lead to any observable collider signatures. The extent to which experimental tests of Newtonian gravity can distinguish this scenario from the scenario of Arkani-Hamed, Dimopoulos, and Dvali with one and two millimeter size extra dimensions is explicitly demonstrated.

Aspects of localized gravity around the soft minima

n-Dimensional pure gravity theory can be obtained as the effective theory of an n+1 model (with non-compact extra dimension) where general n+1 reparametrization invariance is explicitly broken in the extra dimension. As was pointed out in the literature, a necessary consistency condition for having a non-vanishing four dimensional Newton constant is the normalizability in the extra dimension of the zero mass graviton. This, in turn, implies that gravity localization is produced around the local minima of a potential in the extra dimension. We study gravity in the neighborhood of the soft ("thick") local minima.

Kaluza-Klein Reduction in a Warped Geometry Revisited

We study the Kaluza-Klein dimensional reduction of zero-modes of bulk antisymmetric tensor fields on a non-compact extra dimension in the Randall-Sundrum model. It is shown that in the Kaluza-Klein reduction on a non-compact extra dimension we have in general a zero-mode depending on a fifth dimension in addition to a conventional constant zero-mode in the Kaluza-Klein reduction on a circle. We examine the localization property of these zero-modes on a flat Minkowski 3-brane. In particular, it is shown that a 2-form and a 3-form on the brane can be respectively obtained from a 3-form and 4-form in the bulk by taking the zero-mode dependent on the fifth dimension.

Geodesics and Newton’s law in brane backgrounds

In brane world models our universe is considered as a brane embedded into a higher-dimensional space. We discuss the behavior of geodesics in the Randall-Sundrum background and point out that free massive particles cannot stably move along the brane. The brane is repulsive, and matter will be expelled from the brane into the extra dimension. This is undesirable, and hence we study a simple alternative model with a noncompact extra dimension, but with an attractive brane embedded into the higher-dimensional space. We study the linearized gravity equations and show that Newton's gravitational law is valid on the brane also in the alternative background.

Solution to the hierarchy problem with an infinitely large extra dimension and moduli stabilization

We construct a class of solutions to the Einstein's equations for dimensions greater than or equal to six. These solutions are characterized by a non-trivial warp factor and possess a non-compact extra dimension. We study in detail a simple model in six dimensions containing two four branes. One of each brane's four spatial directions is compactified. The hierarchy problem is resolved by the enormous difference between the warp factors at the positions of the two branes, with the standard model fields living on the brane with small warp factor. Both branes can have positive tensions. Their positions, and the size of the compact dimension are determined in terms of the fundamental parameters of the theory by a combination of two independent and comparable effects---an anisotropic contribution to the stress tensor of each brane from quantum fields living on it and a contribution to the stress tensor from a bulk scalar field. One overall fine tuning of the parameters of the theory is required ---that for the cosmological constant.

Solving the hierarchy problem with noncompact extra dimensions

We show that gravitational effects of global cosmic 3-branes can be responsible for compactification from six to four space-time dimensions, naturally producing the observed hierarchy between electroweak and gravitational forces. The finite radius of the transverse dimensions follows from Einstein's equation, and is exponentially large compared with the scales associated with the 3-brane. The space-time ends on a mild naked singularity at the boundary of the transverse dimensions; nevertheless unitary boundary conditions render the singularity harmless.

Dimensional reduction of spacrtime induced by nonlinear scalar dynamics and noncompact extra dimensions

We discuss general aspects of dimensional reduction induced by nonlinear scalar dynamics, including the small fluctuation expansion of the action. The case of compact positively curved scalar manifolds described by symmetric spaces G/H is shown to be free of tachyonic instabilities; the spectrum consists of a graviton, a massless scalar and towers of massive spin-two, spin-one, and spin-zero fields. These towers are worked out explicitly for the case of a two-sphere. The case of noncompact negatively curved scalar manifolds inducing a noncompact nonhomogeneous space for the extra dimensions is studied in the particular example of SU(1,1)/U(1). The massless spectrum consists of a graviton and a scalar and suitable boundary conditions are seen to give a discrete spectrum, actual conservation of formally conserved quantities, and no problems of interpretation. We discuss positive energy.

A two-loop calculation of the mass gap for the O( N) model in finite volume

The mass gap for the quantum O( N) non-linear sigma model in a finite volume in two dimensions is calculated to two-loop order in perturbation theory. This result is used to estimate the mass gap of the infinite-volume O(3) model to be about 2.1 Λ MS ± 10% . The calculation is carried out using dimensional regularization with both compact and non-compact extra dimensions, with the same result in both cases.