The Kaluza and Klein versions of Kaluza-Klein theory are reviewed and compared. The differences in the field equations of the two theories are related to the transformation properties of the metrics employed. Based on this comparison a modified version of the Kaluza theory is proposed, in which the different sectors of the metric which describe gravitation, electromagnetism and the scalar field are considered to be partially separate entities, with distinct coordinate transformation properties. In addition, the cylinder condition is relaxed, so that it only affects the 4-D sector of the metric. This results in a theory in which the gravitational and electromagnetic fields are restricted to a four-dimensional brane, and the scalar field is restricted to the 5-D bulk.
We investigate some properties of string theory on Kaluza-Klein Melvin background. We discuss what happens when closed string tachyons in the theory condense, by using a linear sigma model of the Kaluza-Klein Melvin background.
The enhancement in the decay rate of the Kaluza-Klein vacuum due to the presence of a brane is studied, both in the test brane approximation and beyond it. Spontaneous brane materialization in the Kaluza-Klein vacuum is also described.
We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of Kaluza-Klein black hole. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated, and the microscopic entropy calculated by using Cardy formula agrees with the Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, we investigate the hidden conformal symmetry of Kaluza-Klein black hole by studying the near-region wave equation of a neutral massless scalar field, and find the left and right tempe…
The behavior of small perturbations around the Kaluza-Klein monopole in the five dimensional space-time is investigated. The fact that the odd parity gravitational wave does not propagate in the five dimensional space-time with Kaluza-Klein monopole is found provided that the gravitational wave is constant in the fifth direction.
We study behavior of bulk gauge field in the bigravity model in which two positive tension $AdS_4$ branes in $AdS_5$ bulk are included. We solve the equations of motions for Kaluza-Klein modes and determine the mass spectrum. It is shown that unlike the case of graviton, we find no ultralight Kaluza-Klein modes in the spectrum.
We consider in the paper some consequences of the nonsymmetric Kaluza-Klein (Jordan-Thiry) theory with spontaneous symmetry breaking connecting to the existence of the warp factor and communnication in extra-dimensions. We consider a toy model of a time machine.
We construct the (bosonic) effective worldvolume action of an M-theory Kaluza-Klein monopole in a background given by the bosonic sector of eleven-dimensional massive supergravity, i.e. a "massive Kaluza-Klein monopole". As a consistency check we show that the direct dimensional reduction along the isometry direction of the Taub-NUT space leads to the massive D-6-brane. We furthermore perform a double dimensional reduction in the massless case and obtain the effective worldvolume action of a type IIA Kaluza-Klein monopole.
We perform a numerical study of the four-dimensional spin-2 Kaluza-Klein spectrum of supersymmetric AdS$_4\times S^2(\mathcal{B}_4)$ vacua and show that they do not exhibit scale separation. Our methods are generally applicable to similar problems where the compactification geometry is not known analytically, hence an analytic treatment of the spectrum of Kaluza-Klein masses is not available.
We construct a solution of two black holes on a Kaluza-Klein bubble in Einstein-Maxwell-dilaton theory. We explore the consequences of the presence of charge for the properties of this solution, and obtain a generalized Smarr relation and first law.
We address the question of whether or not fermions with twisted periodicity condition suppress the semiclassical decay of M^4xS^1 Kaluza--Klein vacuum. We consider a toy (1+1)-dimensional model with twisted fermions in cigar-shaped Euclidean background geometry and calculate the fermion determinant. We find that contrary to expectations, the determinant is finite. We consider this as an indication that twisted fermions do not stabilize the Kaluza--Klein vacuum.
The dynamics of chiral p-forms can be captured by a lower-dimensional parity-violating action motivated by a Kaluza-Klein reduction on a circle. The massless modes are (p-1)-forms with standard kinetic terms and Chern-Simons couplings to the Kaluza-Klein vector of the background metric. The massive modes are p-forms charged under the Kaluza-Klein vector and admit parity-odd first-order kinetic terms. Gauge invariance is implemented by a Stueckelberg-like mechanism using (p-1)-forms. A Chern-Simons term for the Kaluza-Klein vector is generated at one loop by massive p-form modes. These findings…
We examine Kaluza-Klein branes in detail. Specifically, we show that codimension four submanifolds that are stationary under a semi-free circle action may be interpreted as branes or antibranes in the Kaluza-Klein reduced space that are magnetically charged under the Kaluza-Klein field strength. We derive the equation in cohomology that is satisfied by such a brane using an explicit construction of the Thom class of the normal bundle of the brane worldvolume in the reduced space. This may be applied to both the D6-brane of Type IIA String Theory, and also to various recent constructions of mag…
Non-supersymmetric black holes carrying both electric and magnetic charge with respect to a single Kaluza-Klein gauge field have much in common with supersymmetric black holes. Angular momentum conservation and other general physics principles underlies some of their basic features. Kaluza-Klein black holes are interpreted in string theory as bound states of D6-branes and D0-branes. The microscopic theory reproduces the full nonlinear mass formula of the extremal black holes.
In this contribution we study the Klein-Gordon oscillator on the curved background within the Kaluza-Klein theory. The problem of interaction between particles coupled harmonically with a topological defects in Kaluza-Klein theory is studied. We consider a series of topological defects, that treat the Klein-Gordon oscillator coupled to this background and find the energy levels and corresponding eigenfunctions in these cases. We show that the energy levels depend on the global parameters characterizing these spacetimes. We also investigate a quantum particle described by the Klein-Gordon oscil…
A fundamental string with non-zero winding number can unwind in the presence of a Kaluza-Klein monopole. We use this fact to deduce the presence of a zero mode for the Kaluza-Klein monopole corresponding to excitations carrying H electric charge and we study the coupling of this zero mode to fundamental strings. We also a describe a T-dual process in which the momentum of a fundamental string ``unwinds'' in the presence of a H monopole. We use the coupling of string winding modes to the dyon collective coordinate of the Kaluza-Klein monopole to argue that there are stringy corrections to the K…
Efforts have been made recently to reformulate traditional Kaluza-Klein theory by using a generalized definition of a higher-dimensional extended space-time. Both electromagnetism and gravity have been studied in this context. We review some of the models which have been proposed, with a special effort to keep the mathematical formalism to a very minimum.
We evaluate the divergent part of the Vilkovisky-DeWitt effective action for Einstein gravity on even-dimensional Kaluza-Klein spacetimes of the form $M^{4}\times S^{N}$. Explicit results are given for $N$=2, 4, and 6. Trace anomalies for gravitons are also given for these cases. Stable Kaluza-Klein configurations are sought, unsuccessfully, assuming the divergent part of the effective action dominates the dynamics.
We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the dependence of metric tensor on reduced dimensions is negligible it becomes a pure antisymmetric tensor.
We point out that in heterotic string theory compactified on a 6-torus, after a consistent truncation of the 10-d gauge fields and the antisymmetric tensor fields, 4-dimensional black holes of Kaluza-Klein theory on a 6-torus constitute a subset of solutions.
The ultra-violet behavior of Kaluza-Klein theories on a one dimensional orbifold is discussed. An extension of dimensional regularization that can be applied to a compact dimension is presented. Using this, the FI-tadpole is calculated in the effective KK theory resulting from compactifying supersymmetric theories in 5 dimensions.
We investigate the zero modes of the Kaluza-Klein monopole in M-theory and show that the Born-Infeld action and the Chern-Simons term of a D6-brane are reproduced to quadratic order in the field strength of the U(1) field on the brane.
Kaluza-Klein reduction of the 3-dimensional gravitational Chern-Simons term leads to a 2-dimensional theory that supports a symmetry breaking solution and an associated kink interpolating between AdS and dS geometries.
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
It is shown that the T-duality in σ-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher's duality transformation interchanges the topological and Noether charges.
The Kaluza-Klein monopole is a well known object in both gravity and string theory, related by T-duality to a "smeared" NS5-brane which retains the isometry around the duality circle. As the true NS5-brane solution is localized at a point on the circle, duality implies that the Kaluza-Klein monopole should show some corresponding behavior. In this paper, we express the Kaluza-Klein monopole as a gauged linear sigma model in two dimensions and show that worldsheet instantons give corrections to its geometry. These corrections can be understood as a localization in "winding space" which could be…
Using the solitonic solution generating techniques, we generate a new exact solution which describes a pair of rotating black holes on a Kaluza-Klein bubble as a vacuum solution in the five-dimensional Kaluza-Klein theory. We also investigate the properties of this solution. Two black holes with topology S^3 are rotating along the same direction and the bubble plays a role in holding two black holes. In static case, it coincides with the solution found by Elvang and Horowitz.
We investigate the properties of non-linear electromagnetism based on the Born-Infeld Lagrangian in multi-dimensional theories of Kaluza-Klein type. We consider flat space-time solutions only, which means that the space-time metric is constant, and the only supplementary variable is the dilaton field, a scalar. We show that in the case of Kaluza-Klein theory, the Born-Infeld Lagrangian describes an interesting interaction between the electromagnetic and scalar fields, whose propagation properties are modified in a non-trivial manner.
We describe new bubble decays in pure D+1 dimensional Einstein theory with two compact directions. The instanton solution is constructed by analytic continuation of the Kaluza-Klein electrically charged black hole solution. We show that the instanton describes the decay of a Kaluza-Klein vacuum M^{D-1} x T^2 with a non-vanishing torus tilt parameter. The decay is produced by the creation of a bubble of nothing which expands with time. We compute the instanton action, which shows that this Kaluza-Klein vacuum becomes more stable as the torus tilt parameter is increased. As an application, we co…
We perform a Kaluza-Klein inspired rewriting of double field theory by splitting the coordinates into `compact' and `non-compact' directions. There is no truncation of the compact coordinates or their duals, and so this formulation is manifestly O(d,d) invariant, with d the number of compact directions. The action can serve as starting point for arbitrary Kaluza-Klein ansaetze. For a torus background the theory describes the full tower of Kaluza-Klein modes or, in the dual frame, of the winding modes. The Kaluza-Klein vector is a gauge field for the duality-covariantized Courant bracket algebr…
Kaluza-Klein theory in which the geometry of an additional dimension is fractal has been considered. In such a theory the mass of an elementary electric charge appears to be many orders of magnitude smaller than the Planck mass, and the "tower" of masses which correspond to higher integer charges becomes aperiodic.
We construct new exact solutions to 5D Einstein-Maxwell equations describing sequences of Kaluza-Klein bubbles and dipole black rings. The solutions are generated by 2-soliton transformations from vacuum black ring - bubble sequences. The properties of the solutions are investigated. We also derive the Smarr-like relations and the mass and tension first laws in the general case for such configurations of Kaluza-Klein bubbles and dipole black rings. The novel moment is the appearance of the magnetic flux in the Smarr-like relations and the first laws.
In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal space, the SO(n) symmetry and SU(n) symmetry are discussed. And the Kaluza-Kl…
The non-Abelian Kaluza-Klein unification of gravitation with gauge fields theory is reformulated, with the inclusion of a massive spin-2 field defined by the extrinsic curvature. The internal space is non-compact, characterized by the group of rotations of vectors orthogonal to the space-time. The non-compactness of the internal space warrants the solution of the fermion chirality problem of the original Kaluza-Klein theory and makes it closer to the more recent Brane World paradigm, in special to the so called DGP model. However, the access of gravitation to the extra dimensions is defined by…
The M-theory interpretation of certain D=10 IIA p-branes implies the existence of worldvolume Kaluza-Klein modes which are expected to appear as 0-brane/p-brane bound states preserving 1/4 of the spacetime supersymmetry. We construct the corresponding solutions of the effective supergravity theory for $p=1,4$, and show that no such solution exists for $p=8$.
We clarify a mechanism to obtain a massless gauge boson from the Kaluza-Klein approach of the Randall-Sundrum(RS) brane world. This corresponds exactly to the same mechanism of achieving a localization of the gauge boson by adding both the bulk and brane mass terms. Accordingly this work puts another example for a localization-mechanism of the gauge boson on the brane.
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-for…
We consider a dynamics of Higgs' Fields in the framework of cosmological models involving a scalar field from Nonsymmetric Kaluza Klein (Jordan-Thiry) Theory. The scalar field plays here a role of a quintessece field. We consider phase transitions in cosmological models of the second and of the first order due to an evolution of Higgs' field. We develop inflationary models including calculation of an amount of an inflation.
In this note we present a closed expression for the space-time effective action for all bosonic fields (massless and massive) obtained from the compactification of gravity or supergravity theories (such as type II or eleven-dimensional supergravities) from $D$ to $d$ space-time dimensions.
The genuine Kaluza-Klein-like theories (with no fields in addition to gravity with torsion) have difficulties with the existence of massless spinors after the compactification of some of dimensions of space\cite{witten}. We demonstrate in this letter on an example of a flat torus - as a compactified part of an (1+5)-dimensional space - that for constant fields and appropriate boundary conditions there exists in the 1+3 dimensional space a massless solution, which is mass protected and chirally coupled with a Kaluza-Klein charge to the corresponding gauge field.
We construct a new exact solution to the 5D Einstein equations describing rotating black ring with a single angular momentum surrounded by two Kaluza-Klein bubbles. The solution is generated by 2-soliton Bäcklund transformation. Its physical properties are computed and analyzed. The corresponding static solution, the rotating black string and the boosted black string are reproduced as limits.
We examine the challenge of viewing all the fields in supergravity as arising from a Kaluza-Klein like dimensional reduction of some higher-dimensional theory. This gives rise to what is known as exceptional field theory or double field theory. A particular emphasis is placed on following the Kaluza-Klein intuition leading to the identification of charged states and a reinterpretation of the central charges. We further give a description of the novel extended geometry as a generalised phase space and the relationship to string and M-theory theory and the notion of quantization
Applying the G_{2(2)} generating technique for minimal D=5 supergravity to the Rasheed black hole solution, we present a new rotating charged Kaluza-Klein black hole solution to the five-dimensional Einstein-Maxwell-Chern-Simons equations. At infinity, our solution behaves as a four-dimensional flat spacetime with a compact extra dimension and hence describes a Kaluza-Klein black hole. In particlar, the extreme solution is non-supersymmetric, which is contrast to a static case. Our solution has the limits to the asymptotically flat charged rotating black hole solution and a new charged rotatin…
We study the hidden conformal symmetry of four-dimensional extremal Kaluza-Klein black hole. The scalar Laplacian corresponding to the radial equation in the near-region is rewritten in terms of the $SL(2,\mathbb R)$ quadratic Casimir. Using the first law of black hole thermodynamics, this symmetry enables us to obtain the conjugate charges for the CFT side. The real-time correlators are also found to agree with the CFT expectations.
All regular four-dimensional black holes are constructed in the theory obtained by Kaluza-Klein reduction of five-dimensional Einstein gravity. They are interpreted in string theory as rotating bound states of D0- and D6-branes. Conservation of angular momentum is important for the stability of the bound states. The thermodynamics, the duality symmetries, and the near-horizon limit are explored.
The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for th…
We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five dimensional vacuum Einstein equations. Using both numerical and analytical methods we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi IX ansatz recently introduced in \cite{bcs}. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of BPS states in M/String theory is briefly discussed.
The transition from formulations with extra dimensions to Kaluza-Klein theories, aimed at extending the Standard Model, bears the ingredients of hidden symmetries and the Kaluza-Klein mechanism for mass generation. We explore these essential aspects in detail, and find that much can be said about them with no reference to the specific geometry of compact extra dimensions: the low-energy theory is determined, included dynamic variables and symmetries; mass terms arise; eigenfunctions that define Kaluza-Klein fields are fixed by the appropriate choice a Casimir invariant; there is a set of Kaluz…
We use local counterterm prescriptions for asymptotically flat space to compute the action and conserved quantities in five-dimensional Kaluza-Klein theories. As an application of these prescriptions we compute the mass of the Kaluza-Klein magnetic monopole. We find consistent results with previous approaches that employ a background subtraction.
The Kaluza-Klein idea of extra spacetime dimensions continues to pervade current attempts to unify the fundamental forces, but in ways somewhat different from that originally envisaged. We present a modern perspective on the role of internal dimensions in physics, focussing in particular on superstring theory. A novel result is the interpretation of Kaluza-Klein string states as extreme black holes.(Talk delivered at the Oskar Klein Centenary Nobel Symposium, Stockholm, September 19-21, 1994.)
Using the SL(2,R)-duality in a dimensionally reduced spacetime in (the bosonic sector of) five-dimensional minimal supergravity, we construct general Kaluza-Klein black hole solutions which carry six independent charges, its mass, angular momentum along four dimensions, electric and magnetic charges of the Maxwell fields in addition to Kaluza-Klein electric and magnetic monopole charges.
An analysis of the effects associated with the Kaluza-Klein excitations of the photon and of the W and Z bosons on g_μ-2 for d number of extra dimensions with large radius compactifications is given. The Kaluza-Klein effects on g_μ-2 are found to be very sensitive to the number of extra dimensions. For models where the quark-lepton generations live on the 4D wall, it is shown that when the constraints from the Kaluza-Klein corrections to the Fermi constant are included, the effects of the Kaluza-Klein excitations to g_μ-2 become too small to be observable. A model which evades Kaluza-Klein cor…
We explore the possibility that the Kaluza-Klein graviton states induce electroweak symmetry breaking. We also demonstrate that electroweak symmetry breaking could have a large impact on KK phenomenology.
We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3)$\,\times\,$SO(3)-invariant AdS$_4$ vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional ${\cal N}=8$ supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS$_4$ vacuum is perturbatively unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, which …
We explore the obsevability of extra dimensions through 5-dimensional squashed Kaluza-Klein black holes residing in the Kaluza-Klein spacetime. With the expectation that the Hawking radiation reflects the 5-dimensional nature of the squashed horizon, we study the Hawking radiation of a scalar field in the squashed black hole background. As a result, we show that the luminosity of Hawking radiation tells us the size of the extra dimension, namely, the squashed Kaluza-Klein black holes open a window to extra dimensions.
We present a Kaluza-Klein reduction for the Unruh response that a brane, in an AdS bulk would experience due to its acceleration. The Unruh radiation is realised as particle production on the brane for each of the Kaluza-Klein modes. A correction, coming from the massive modes, is calculated for the standard Unruh effect in Minkowski spacetime and it is found that the response coming from these modes is exponentially suppressed.
We consider the Newton's force law for brane world consisting of periodic configuration of branes. We show that it supports a massless graviton. Furthermore, this massless mode is well separated from the Kaluza-Klein spectrum by a mass gap. Thus most of the problems in phenomenology coming from continuum of Kaluza-Klein modes without mass gap are potentially cured in such a model.
