Finite temperature Casimir effect in spacetime with extra compactified dimensions

In this Letter, we derive the explicit exact formulas for the finite temperature Casimir force acting on a pair of parallel plates in the presence of extra compactified dimensions within the framework of Kaluza–Klein theory. Using the piston analysis, we show that at any temperature, the Casimir force due to massless scalar field with Dirichlet boundary conditions on the plates is always attractive and the effect of extra dimensions becomes stronger when the size or number of the extra dimensions increases. These properties are not affected by the explicit geometry and topology of the Kaluza–Klein space.     

Charged black holes on Kaluza–Klein bubbles

We construct exact solutions of the Einstein–Maxwell field equations in five dimensions, which describe general configurations of charged and static black holes sitting on a Kaluza–Klein bubble. More specifically we discuss the configurations describing two black holes sitting on a Kaluza–Klein bubble and also the general charged static black Saturn balanced by a Kaluza–Klein bubble. A straightforward extension of the solution-generating technique leads to a new solution describing the charged static black Saturn on the Taub-bolt instanton. We compute the conserved charges and investigate some of the thermodynamic properties of these systems.     

The Casimir force on a piston in the spacetime with extra compactified dimensions

A Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in high-dimensional spacetimes within the frame of Kaluza–Klein theory is analyzed. We derive and calculate the exact expression for the Casimir force on the piston. We also compute the Casimir force in the limit that one outer plate is moved to the extremely distant place to show that the reduced force is associated with the properties of additional spatial dimensions. The more dimensionality the spacetime has, the stronger the extra-dimension influence is. The Casimir force for the piston in the model including a third plate under the background with extra compactified dimensions always keeps attractive. Further we find that when the limit is taken the Casimir force between one plate and the piston will change to be the same form as the corresponding force for the standard system consisting of two parallel plates in the four-dimensional spacetimes if the ratio of the plate-piston distance and extra dimensions size is large enough.     

Kinematical test of large extra dimension in beta decay experiments

The forthcoming experiments on neutrino mass measurement using beta decay, open a new window to explore the large extra dimension model. The Kaluza–Klein tower of neutrinos in large extra dimension contributes to the Kurie function of beta decay that can be tested kinematically. In addition to providing an alternative approach using just the kinematical properties, we show that KATRIN can probe the compactification radius of extra dimensions down to 0.2 μm which is better, at least by a factor of two, than the upper limits from neutrino oscillation experiments.     

Entropy of Kaluza–Klein black hole from Kerr/CFT correspondence

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four-dimensional Kaluza–Klein black hole in Einstein–Maxwell–Dilaton theory. For the extremal Kaluza–Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein–Hawking entropy of extremal Kaluza–Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza–Klein black hole, and find the left and right temperatures of the dual conformal field theory. Furthermore, we find that the entropy of non-extremal Kaluza–Klein black hole is reproduced by Cardy formula.     

Getting to the top with extra dimensions

The prospect of large extra dimensions and an effective theory of gravity at around a TeV has interesting experimental consequences. In these models, the Kaluza–Klein modes interact with Standard Model particles and these interactions lead to testable predictions at present and planned colliders. We investigate the effect of virtual exchanges of the spin-2 Kaluza–Klein modes in the production cross-section of pairs at the Tevatron and the LHC and find that the cross-section can be an effective probe of the large extra dimensions. This enables us to put bounds on the effective low-energy scale.     

Kaluza–Klein modes of bulk fields in a generalized Randall–Sundrum scenario

We consider a generalised two brane Randall–Sundrum model with non-zero cosmological constant on the visible TeV brane. Massive Kaluza–Klein modes for various bulk fields namely graviton, gauge field and antisymmetric second rank Kalb–Ramond field in a such generalized Randall–Sundrum scenario are determined. The masses for the Kaluza–Klein excitations of different bulk fields are found to depend on the brane cosmological constant indicating interesting consequences in warped brane particle phenomenology.     

Geometric bounds on Kaluza–Klein masses

We point out geometric upper and lower bounds on the masses of bosonic and fermionic Kaluza–Klein excitations in the context of theories with large extra dimensions. The characteristic compactification length scale is set by the diameter of the internal manifold. Based on geometrical and topological considerations, we find that certain choices of compactification manifolds are more favored for phenomenological purposes. Received: 11 August 2000 / Revised version: 30 January 2001 / Published online: 3 May 2001     

Efficient coannihilation process through strong Higgs self-coupling in LKP dark matter annihilation

We point out that the lightest Kaluza–Klein particle (LKP) dark matter in universal extra dimension (UED) models efficiently annihilates through the coannihilation process including the first KK Higgs bosons when the Higgs mass is slightly heavy as 200–230 GeV, which gives the large Higgs self-coupling. The large self-coupling naturally leads the mass degeneracy between the LKP and the first KK Higgs bosons and large annihilation cross sections of the KK Higgs bosons. These are essential for the enhancement of the annihilation of the LKP dark matter, which allows large compactification scale ∼1 TeV to be consistent with cosmological observations for the relic abundance of dark matter. We found that the thermal relic abundance of the LKP dark matter could be reconciled with the stringent constraint of electroweak precision measurements in the minimal UED model.     

Universal features of dimensional reduction schemes from general covariance breaking

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza–Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces, thus fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza–Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza–Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors.     

Geometrization of the Gauge Connection within a Kaluza–Klein Theory

We geometrize a generic (abelian and non-abelian) gauge coupling within the framework of a Kaluza–Klein theory, by choosing a suitable matter-field dependence on the extra coordinates. We first extend the Nöther theorem to a multidimensional spacetime, the Cartesian product of a 4-dimensional Minkowski space and a compact homogeneous manifold (whose isometries reflect the gauge symmetry). On such a “vacuum” configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra for a spacetime with the Kaluza–Klein restrictions. By splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms arise.     

Gravitational scattering in the ADD model revisited

It is argued that the assumption that the standard model particles live on a finite brane in the ADD model does in itself imply a finite propagator for virtual Kaluza–Klein mode exchange. The part of the propagator relevant for large distance scattering is cut-off-independent for scattering at distances large compared to the brane width. The matrix element corresponding to this part can also, at least for an odd number of extra dimensions, be Fourier transformed to position space, giving back the extra-dimensional version of Newton’s law. For an even number of extra dimensions a corresponding result is found by requiring that Newton’s law should be recovered. PACS 04.50.+h; 11.10.Kk; 11.25.Mj     

Tensor gauge field localization on a string-like defect

This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb–Ramond field. In contrast to what happens in Randall–Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza–Klein decomposition, which provides new details about the KK masses.     

On the Klein–Gordon Equation in Higher Dimensions: Are Particle Masses Variable?

We consider ways to generalize the 4D Klein–Gordon equation of particle physics to higher dimensions. The most promising approach implies that the mass which appears in the 4D relation is a term in the source-free 5D relation. We check this explicitly for the case of exact solitonic and cosmological solutions of the Kaluza–Klein equations. In general, particle masses are variable; but are constant for the Schwarzschild and late-universe cases, in agreement with data from the solar system and astrophysics. Our results have significant implications for cosmology, and can easily be extended to 10D superstrings, 11D supergravity and higher dimensions.     

Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze locally anisotropic configurations modeled by anholonomic frames with associated nonlinear connections in general relativity, affine–Poincarè and/or de Sitter gauge gravity and Kaluza–Klein theories. A suitable geometrical formalism for theories with higher order anisotropies and non compactified extra dimensions is introduced. We give a mostly self–containing review of some aspects of gauge models of gravity and discuss their anholonomic generalizations and the conditions of equivalence with the Einstein gravity in arbitrary dimensions. New classes of cosmological solutions describing Friedmann–Robertson–Walker like universes with resolution ellipsoid or torus symmetry.     

Prospects for identification the direct and indirect effects of extra spatial dimensions at the Large Hadron Collider

The existence of massive graviton states, that may be produced as real and virtual particles in high-energy proton collisions, is predicted by the modern developments of Kaluza–Klein models with extra spatial dimensions. The direct and indirect signatures of large and warped extra spatial dimensions may be revealed by analyzing the specific characteristics of dilepton and diphoton final states formed in proton–proton collisions at the Large Hadron Collider (LHC). Virtual effects in the Kaluza–Klein models with large extra spatial dimensions can be discovered by the specic behavior of the dilpton and diphoton invariant-mass distributions, and their identication (in case of discovery) can be performed by the analysis of their angular distributions with integrated center-edge asymmetry. Assuming the nominal values of the LHC collision energy (14 TeV) and luminosity (100 fb^–1), for the models with large extra spatial dimensions we find that the sensitivity to the cutoff parameter M _S will extend up to 8.5 and 7.6 TeV for their discovery and identification, respectively. For the Randall–Sundrum model with a warped extra dimension, the LHC experiments will be sensitive to the graviton resonance with mass up to 4.4 and 3.1 TeV for its discovery and identification, respectively.     

The Energy of Asymptotically de Sitter Spacetimes in Kaluza—Klein Theory

We use a Hamiltonian approach to derive a general expression for 5D Kaluza—Klein metrics which depend on the extra coordinate but whose 4D embedded spacetimes are asymptotically de Sitter. This enables us to better understand the nature of the cosmological constant and the role played by the dimension in inducing 4D matter from 5D geometry.     

Extremal static AdS black hole/CFT correspondence in gauged supergravities

A recently proposed holographic duality allows the Bekenstein–Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza–Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions.     

Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects.     

Non-relativistic holography and singular black hole

We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton–Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza–Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be non-zero.