Torsion-induced gauge field doubling in Kaluza-Klein theory

Torsion in Kaluza-Klein theory is considered. It is shown that a part of the components of the torsion tensor can be identified with the components of gauge fields different from the gauge fields of the Kaluza-Klein theory, while the other part can be identified with the field strength tensor of these gauge fields. The gauge fields introduced this way acquire a geometrically induced mass. It is shown that the torsion in the internal space allows to generate any a priori given mass in Kaluza-Klein theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–15, June, 1988.In conclusion, I want to thank Yu. S. Vladimirov for a discussion of the results of this paper.     

Generalizations of gravitational theory based on group covariance

The mathematical structure, the field equations, and fundamentals of the kinematics of generalizations of general relativity based on semisimple invariance groups are presented. The structure is that of a generalized Kaluza-Klein theory with a subgroup as the gauge group. The group manifold with its Cartan-Killing metric forms the source-free solution. The gauge fields do not vanish even in this case and give rise to additional modes of free motion. The case of the de Sitter groups is presented as an example where the gauge field is tentatively assumed to mediate a spin interaction and give rise to spin motion. Generalization to the conformal group and a theory yielding features of Dirac's large-number hypothesis are discussed. The possibility of further generalizations to include fermions are pointed out. The Kaluza-Klein theory is formulated in terms of principal fibre bundles which need not to be trivial.     

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.     

General relativistic theory of gravitation exhibiting complete group covariance

The geometry of the group manifold is generalized to allow the construction of a general relativistic theory exhibiting all the degrees of freedom of the group in its dynamical variables. The theory has features of a multidimensional Kaluza-Klein theory with noncommuting Killing vectors. The resulting fields suggest, however, a teleparallelistic formulation. The geometry and gauge invariance of the theory are discussed.     

Plane-wave solutions in higher-dimensional Kaluza-Klein theories

Exact solutions representing mixed plane-gravitational waves and planewaves of scalar fields and non-Abelian gauge fields in higher-dimensional Kaluza-Klein theories are obtained under the generalized higher-dimensional harmonic condition. Two special cases are discussed.     

Finsler and Kaluza-Klein gauge theories

A comparison of Kaluza-Klein and Finsler-type gauge theories is sketched. It is shown that the two can be related by a mapping between fiber spaces which is equivalent to a transformation from one representation of the gauge group to another. The Finsler theory lends itself to an interpretation of the mapping operators as being geometrically similar to Yang-Mills potentials. The equations of motion in this theory contain fields which are comparable to connections instead of curvatures. This gives a new geometrical framework for unified field theories.     

Vacuum Stability in Kaluza-Klein Geometric Sigma Models

In Kaluza-Klein geometric sigma models, the scalar fields coupled to higher-dimensional gravity are pure gauge. The gauge fixed theory contains no matter fields, and can consistently be reduced to 4 dimensions, provided the internal space is chosen in the form of a group manifold. The effective 4-dimensional theory includes standard Einstein and Yang-Mills sectors, and is free of the classical cosmological constant problem. In this paper, the stability of the internal excitations is analyzed. It is shown that the initial Lagrangian can be modified to lead to a classically stable effective 4-dimensional theory, independently of the particular group used, and retaining all the basic features of the unmodified theory.     

High energy field theory in truncated anti-de Sitter space

In this Letter we show that in five-dimensional anti-de Sitter (AdS) space truncated by boundary branes, effective field theory techniques are reliable at high energy (much higher than the scale suggested by the Kaluza-Klein mass gap), provided one computes suitable observables. We argue that in the model of Randall and Sundrum for generating the weak scale from the AdS warp factor, the high energy behavior of gauge fields can be calculated in a cutoff independent manner, provided one restricts Green's functions to external points on the Planck brane. Using the AdS/CFT (conformal field theory) correspondence, we calculate the one-loop correction to the Planck brane gauge propagator due to charged bulk fields. These effects give rise to nonuniversal logarithmic energy dependence for a range of scales above the Kaluza-Klein gap.     

An alternative method of reduction to four-dimensional space in Kaluza-Klein theory

A method for constructing gauge field theories with spontaneous symmetry breaking is suggested, and applied to the theory of Kaluza-Klein type. It is shown that the method naturally leads to the appearance of fields and a lagrangian, providing spontaneous breaking of the gauge invariance. The method also allows one to interpret in a novel way the nature of the extra dimensions of space.     

A study of the Higgs effect in the five-dimensional Kaluza-Klein theory

The complete expression of the five-dimensional Einstein-Hilbert action as an expansion in fields in the Appelquist-Chodos parametrization of the Kaluza-Klein metric has been given in this paper. It is explicitly shown that a unitary gauge can be fixed in which in each of the charge sectors the vector and the scalar fields are absorbed as Goldstone modes leaving behind the Pauli-Fierz Lagrangian for massive charged spin-2 field.     

Partially composite two-Higgs doublet model

In the extra dimensional scenarios with gauge fields in the bulk, the Kaluza-Klein (KK) gauge bosons can induce Nambu-Jona-Lasinio (NJL) type attractive fourfermion interactions, which can break electroweak symmetry dynamically with accompanying composite Higgs fields. We consider a possibility that electroweak symmetry breaking (EWSB) is triggered by both a fundamental Higgs and a composite Higgs arising in a dynamical symmetry breaking mechanism induced by a new strong dynamics. The resulting Higgs sector is a partially composite two-Higgs doublet model with specific boundary conditions on the coupling and mass parameters originating at a compositeness scale Λ. The phenomenology of this model is discussed including the collider phenomenology at LHC and ILC.      

Centrifugal deformations of the gravitational kink

The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.     

Field theory in two-time physics with N=1 supersymmetry

We construct N=1 supersymmetric (SUSY) field theory in 4+2 dimensions compatible with the theoretical framework of two-time (2T) physics and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by SUSY and 2T physics gauge symmetries. In a particular gauge the 4+2 theory reduces to ordinary supersymmetric field theory in 3+1 dimensions without any Kaluza-Klein remnants, but with some additional constraints in 3+1 dimensions of interesting phenomenological relevance. This construction is another significant step in the development of 2T physics as a structure that stands above 1T physics.     

Vanishing of the cosmological constant in non-Abelian Kaluza-Klein theories

We present a new approach to the unification of gravity and non-Abelian gauge fields in the framework of Kaluza-Klein theory. It consists in introducing a new connection on the (n + 4)-dimensional manifoldP (metrized principal fiber bundle). This connection is metrical, but with nonvanishing torsion. An enormous cosmological term in the Einstein equations vanishes due to this connection. The new connection simultaneously cancels Planck's mass term in the Dirac equation for the five-dimensional case. The usual interpretation of geodesic equations is still valid.     

Kaluza-Klein dark matter

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard positrons, neutrinos, and photons with unsuppressed rates. Direct detection signals are also promising. These conclusions are generic to bosonic dark matter candidates.     

The Vilkovisky-DeWitt effective action for quantum gravity

The Vilkovisky-DeWitt effective action for gauge theories is reviewed and then discussed in the context of N-dimensional quantum gravity and quantum Kaluza-Klein theory. The formalism gives an effective action which is gauge-independent and gauge and field-parametrization invariant. These features are illustrated for the vacuum energy of N-dimensional gravity. The Bunch-Parker local momentum space approach is used to calculate also the induced Ricci scalar term in the expansion of the effective action in powers of the curvature. The effective field equations are applied to the self-consistent dimensional reduction of five-dimensional Kaluza-Klein theory. A solution exists, but is found to be physically unacceptable.     

Fuzzy Kaluza-Klein induced M2?s from a single M5

We propose an algorithmic procedure of obtaining multiple M2 brane dynamics starting with an action of a single M5 brane. The procedure involves a novel Kaluza-Klein reduction. First, the M5 brane action is truncated to keep a few leading terms in the derivative expansion. Then 3+3 splitting of dimensions is carried out. With expansion in terms of the S² spherical harmonics, the fields are associated with SU(N) (or its infinite extension) gauge algebra. We present an elaborate reduction procedure that leads to ABJM theory when the fuzzy spherical harmonics are replaced by SU(N) gauge generators.     

A geometrical theory of spin motion

A discussion of the fundamental interrelation of geometry and physical laws with Lie groups leads to a reformulation and heuristic modification of the principle of inertia and the principle of equivalence, which is based on the simple de Sitter group instead of the Poincaré group. The resulting law of motion allows a unified formulation for structureless and spinning test particles. A metrical theory of gravitation is constructed with the modified principle, which is structured after the geometry of the manifold of the de Sitter group. The theory is equivalent to a particular Kaluza-Klein theory in ten dimensions with the Lorentz group as gauge group. A restricted version of this theory excludes torsion. It is shown by a reformulation of the energy momentum complex that this version is equivalent to general relativity with a cosmologic term quadratic in the curvature tensor and in which the existence of spinning particle fields is inherent from first principles. The equations of the general theory with torsion are presented and it is shown in a special case how the boundary conditions for the torsion degree of freedom have to be chosen such as to treat orbital and spin angular momenta on an equal footing. The possibility of verification of the resulting anomalous spin-spin interaction is mentioned and a model imposed by the group topology ofSO(3,2) is outlined in which the unexplained discrepancy between the magnitude of the discrete valued coupling constants and the gravitational constant in Kaluza-Klein theories is resolved by the identification of identical fermions as one orbit. The mathematical structure can be adapted to larger groups to include other degrees of freedom.     

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

An important feature of Kaluza-Klein theories is their ability to relate fundamental physical constants to the radii of higher dimensions. In previous Kaluza-Klein theory, which unifies the electromagnetic field with gravity as dimensionless components of a Kaluza-Klein metric, i) all fields have the same physical dimensions, ii) the Lagrangian has no explicit dependence on any physical constants except mass, and hence iii) all physical constants in the field equations except for mass originate from geometry. While it seems natural in Kaluza-Klein theory to add fermion fields by defining higher-dimensional bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do not satisfy conditions (i), (ii), and (iii). In this paper, we show how conditions (i), (ii), and (iii) can be satisfied by including bispinor fields in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor equation, since conditions (i), (ii), (iii) imply a special relation among the terms in the Kaluza-Klein or teleparallel Lagrangian that would not be satisfied in general.