Kaluza-Klein Scheme Research Articles

Kaluza–Klein reduction on a maximally non-Riemannian space is moduli-free

We propose a novel Kaluza–Klein scheme which assumes the internal space to be maximally non-Riemannian, meaning that no Riemannian metric can be defined for any subspace. Its description is only possible through Double Field Theory but not within supergravity. We spell out the corresponding Scherk–Schwarz twistable Kaluza–Klein ansatz, and point out that the internal space prevents rigidly any graviscalar moduli. Plugging the same ansatz into higher-dimensional pure Double Field Theory and also to a known doubled-yet-gauged string action, we recover heterotic supergravity as well as heterotic worldsheet action. In this way, we show that 1) supergravity and Yang–Mills theory can be unified into higher-dimensional pure Double Field Theory, free of moduli, and 2) heterotic string theory may have a higher-dimensional non-Riemannian origin.

EXTRA DIMENSIONS WITH NONTRIVIAL TORSION AND SPINS OF COSMIC STRINGS

As two generalizations of Einstein's general relativity, the nontrivial spacetime torsion and the compact extra dimensions have been largely studied in the literature. In this paper, by combining a torsioned Kaluza–Klein scheme and the field-theory cosmic string theory, we discuss that a higher-dimensional torsion component can be expressed in terms of the usual four-dimensional field strength two-form, and this torsion form can then get trapped into the cores of the cosmic strings and further relate to the intrinsic spins of the strings.

THE EINSTEIN–YANG–MILLS EQUATIONS FROM BIANCHI IDENTITIES

We suggest a novel extension to the Kaluza–Klein scheme that allows us to obtain consistently all SU (n) Einstein–Yang–Mills theories. This construction is based on allowing the five-dimensional spacetime to carry some nonvanishing torsion; however, the four-dimensional spacetime remains intrinsically torsion-free.

ON THE KALUZA–KLEIN GEOMETRIZATION OF THE ELECTROWEAK MODEL WITHIN A GAUGE THEORY OF THE FIVE-DIMENSIONAL LORENTZ GROUP

The geometrization of the Electroweak Model is achieved in a five-dimensional Riemann–Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. U (1) weak hypercharge gauge fields are obtained from a Kaluza–Klein scheme, while the tetradic projections of the extradimensional contortion fields are interpreted as SU (2) weak isospin gauge fields. SU (2) generators are derived by the identification of the weak isospin current to the extradimensional current term in the Lagrangian density of the local Lorentz group. The geometrized U (1) and SU (2) groups will provide the proper transformation laws for bosonic and spinorial fields. Spin connections will be found to be purely Riemannian.

Gravitational theory without the cosmological constant problem

We develop the principle of nongravitating vacuum energy, which is implemented by changing the measure of integration from $\sqrt{-g}d^{D}x$ to an integration in an internal space of $D$ scalar fields $\phi_{a}$. As a consequence of such a choice of the measure, the matter Lagrangian $L_{m}$ can be changed by adding a constant while no cosmological term is induced. Here we develop this idea to build a new theory which is formulated through the first order formalism, i.e. using vielbein $e_{a}^{\mu}$ and spin connection $\omega_{\mu}^{ab}$ (a,b=1,2,...D) as independent variables. The equations obtained from the variation of $e_{a}^{\mu}$ and the fields $\phi_{a}$ imply the existence of a nontrivial constraint. This approach can be made consistent with invariance under arbitrary diffeomorphisms in the internal space of scalar fields $\phi_{a}$ (as well as in ordinary space-time), provided that the matter model is chosen so as to satisfy the above mentioned constraint. If the matter model is not chosen so as to satisfy automatically this constraint, the diffeomorphism invariance in the internal space is broken. In this case the constraint is dynamically implemented by the degrees of freedom that become physical due to the breaking of the internal diffeomorphism invariance. However, this constraint always dictates the vanishing of the cosmological constant term and the gravitational equations in the vacuum coincide with vacuum Einstein's equations with zero cosmological constant. The requirement that the internal diffeomorphisms be a symmetry of the theory points towards the unification of forces in nature like in the Kaluza-Klein scheme.

TOWARDS A CONSISTENT FOUR-DIMENSIONAL SUPERSTRING (I)

A Kaluza-Klein “compactification” Ansatz is applied to the D=10, N=1, heterotic, Green-Schwarz superstring to produce a D=4, N=4 theory. It is demonstrated that κ symmetry is preserved under the procedure, a necessary condition for the 4D theory to retain the consistency of the 10D one. This is the first time that the Kaluza-Klein scheme has been reported to have been applied to superspace.

Some comments on torsion in the Kaluza-Klein scheme

It is shown that in the five-dimensional Kaluza-Klein theory with torsion, a severe constraint on the Maxwell fields arises when the torsion potential is related to the usual scalar field. It is further pointed out that the Kaluza-Klein scheme provides a natural explanation of the fact that torsion does not couple to spin-1 gauge fields.

Some global properties and invariance of bundle metrics in the Kaluza–Klein scheme

It is shown that the transition functions that give the global structure of the fiber bundle play an important role in the construction of the metric. The invariance properties of this metric under general gauge transformations are discussed and it is found that the usual requirement of a gauge-invariant metric leads to severe constraints on the gauge fields. To avoid them, it is shown that the metric should instead be covariant with respect to these transformations. Moreover the existence of global actions that are essential in the context of the consistency problem is also discussed. The presence of such actions is studied in both the principal and their associated bundles. In the case of a homogeneous bundle with G/H as the typical fiber, it is shown that a ‘‘spliced’’ bundle with G×N(H)/H as the structure group has to be used. The unified space is then taken as the bundle space of its associated bundle.

Consistency of the G-invariant Kaluza-Klein scheme

We consider the G-invariant Kaluza-Klein scheme on M × G/H leading to the N(H)/H gauge group and demonstrate its consistency. The full-scale ansatz with G × N(H)/H gauge bosons from M × G/H compactification is argued to be, in general, inconsistent.

Fermion masses in a generalized Kaluza-Klein theory

The problem of introducing light fermions in the Kaluza-Klein scheme is investigated in a model recently proposed by Rubakov and Shaposhnikov. We show that there is a specific mechanism of having light fermions in this model and find, as a concrete example, a solution in six dimensions which allows light fermions and has ${S}^{2}$ symmetry. The problems associated with this solution are pointed out.

Monopole-fermion dynamics and the Rubakov effect in Kaluza-Klein theories

The dynamical property of a charged fermion is analyzed in the background field of a monopole in the five-dimensional Kaluza-Klein theory. It is proved that the hamiltonian is hermitian in each charge sector, in contrast with the same problem in QED. This suggests that the Rubakov effect will not occur if the true unified theory is to be given by the Kaluza-Klein scheme.