Kaluza-Klein Research Articles

Kaluza–Klein dimensional reduction from elasticity theory of crumpled paper

During the last century, two theories using the concept of dimensional reduction have been developed independently. The first, known as Föppl–von Kármán theory, uses Riemannian geometry and continuum mechanics to study the shaping of thin elastic structures which could become as complex as crumpled paper. The second one, known as Kaluza–Klein theory, uses Minkowskian geometry and general relativity to unify fundamental interactions and gravity under the same formalism. Here we draw a parallel between these two theories in an attempt to use concepts from elasticity theory of plates to recover the Einstein–Maxwell equations. We argue that Kaluza–Klein theory belongs to the same conceptual group of theories as three-dimensional elasticity, which upon dimensional reduction leads to the Föppl–von Kármán theory of two-dimensional elastic plates. We exploit this analogy to develop an alternative Kaluza–Klein formalism in the framework of elasticity theory in which the gravitational and electromagnetic fields are, respectively, associated with stretching-like and bending-like deformations. We show that our approach of dimensional reduction allows us to retrieve the Lagrangian densities of both gravitational, electromagnetic and Dirac spinors fields as well as the Lagrangian densities of mass and charge sources.

Monstrous M-Theory

In 26+1 space–time dimensions, we introduce a gravity theory whose massless spectrum can be acted upon by the Monster group when reduced to 25+1 dimensions. This theory generalizes M-theory in many respects, and we name it Monstrous M-theory, or M2-theory. Upon Kaluza–Klein reduction to 25+1 dimensions, the M2-theory spectrum irreducibly splits as 1 ⊕ 196,883, where 1 is identified with the dilaton, and 196,883 is the dimension of the smallest non-trivial representation of the Monster. This provides a field theory explanation of the lowest instance of the Monstrous Moonshine, and it clarifies the definition of the Monster as the automorphism group of the Griess algebra by showing that such an algebra is not merely a sum of unrelated spaces, but descends from massless states for M2-theory, which includes Horowitz and Susskind’s bosonic M-theory as a subsector. Further evidence is provided by the decomposition of the coefficients of the partition function of Witten’s extremal Monster SCFT in terms of representations of SO24, the massless little group in 25+1; the purely bosonic nature of the involved SO24-representations may be traced back to the unique feature of 24 dimensions, which allow for a non-trivial generalization of the triality holding in 8 dimensions. Last but not least, a certain subsector of M2-theory, when coupled to a Rarita–Schwinger massless field in 26+1, exhibits the same number of bosonic and fermionic degrees of freedom; we cannot help but conjecture the existence of a would-be N=1 supergravity theory in 26+1 space–time dimensions.

β Symmetry of Supergravity.

Continuous O(d,d) global symmetries emerge in Kaluza-Klein reductions of D-dimensional string supergravities to D-d dimensions. We show that the nongeometric elements of this group effectively act in the D-dimensional parent theory as a hidden bosonic symmetry that fixes its couplings: the β symmetry. We give the explicit β transformations to first order in α^{'} and verify the invariance of the action as well as the closure of the transformation rules.

Effective action of a self-interacting scalar field on brane

In extra dimensional theories, the four-dimensional field theory is reduced from a fundamental field theory in the bulk spacetime by integrating the extra dimensional part. In this paper we investigate the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario. We consider two typical thick brane solutions and obtain the Pöschl–Teller and harmonic potentials of the Kaluza–Klein (KK) modes, respectively. The analytical mass spectra and wave functions along extra dimension of the KK modes are obtained. Further, the effective coupling constant between different KK particles, cross section, and decay rate for some processes of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. Some interesting properties of these interactions are found with these calculations. The KK particles with higher mode have longer lifetime, and they almost do not interact with ordinary matter on the brane if their mode numbers are large enough. Thus, these KK particles with higher modes might be a candidate of dark matter.

Connection dynamics of reduced five-dimensional Kaluza-Klein theory and its deparametrization

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.

Five-dimensional strange quark matter cosmological model with string cloud

The work in this paper is devoted to the study of Kaluza–Klein (KK) cosmological model with strange quark matter attached to string cloud in the framework of metric version of [Formula: see text] gravity. By utilizing hybrid expansion law for average scale factor of the model i.e. [Formula: see text], here [Formula: see text] and [Formula: see text] are positive constants, we derive the solution of the field equations of KK model in the [Formula: see text] gravity. Various dynamical parameters of the model are obtained and their behavior is analyzed through graphical representation. We observe that the analysis of deceleration parameter exhibits a smooth transition of the universe from early decelerated phase to current accelerated epoch. Also, we discussed well-known state-finder parameters [Formula: see text] and [Formula: see text] planes which are analyzed by graphical representation.

Evolution of scalar field resonances in a braneworld

In this work, we investigate the numerical evolution of massive Kaluza–Klein (KK) modes of a scalar field in a thick brane. We derive the Klein–Gordon equation in five-dimensional spacetime, and obtain the evolution equation and the Schrödinger-like equation. With the resonances of the scalar KK modes as the initial data, the scalar field is evolved with the maximally dissipative boundary condition. The results show that there are scalar KK resonant particles with long life on the brane, which indicates that these resonances might be regarded as a candidate for dark matter.

On the Lagrangian holographic relation at D → 2 and 4 limits of gravity

The gravitational Lagrangian can be written as a summation of a bulk and a total derivative term. For some theories of gravity such as Einstein gravity, or more general Lovelock gravities, there are Lagrangian holographic relations between the bulk and the total derivative term such that the latter is fully determined by the former. However at the D→2&4 limit, the bulks of Einstein or Gauss-Bonnet theories become themselves total derivatives. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities gives rise to some two-dimensional or four-dimensional scalar-tensor theories respectively. We obtain the holographic relations for the D=2 and D=4 cases, which have the same form as the holographic relations in pure gravity in the foliation independent formalism.

T-duality of D-brane versus O-plane actions

It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T-duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order α′ and higher, the T-duality is satisfied only for a subclass of the couplings for arbitrary base space background. They are m = 0 couplings where m is the number of overset{sim }{B} -field (without derivative on it). For m > 0 couplings, the base space metric must be block-diagonal and the momentum U(1) vector field in the transverse reduction must be zero. However, the derivatives of the metric and the vector field are arbitrary.Using the assumption that the effective actions at the critical dimension are background independent, we then show that the T-duality constraint for the couplings at order α′ and for m = 0, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive α′-correction. We have also imposed the T-duality constraint on m = 1, 2, 3, 4 couplings. Because of the above restriction on the base space background in these cases, however, the T-duality can only partially fix the couplings for m > 0. This study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order α′.

On global smooth small data solutions of 3-D quasilinear Klein-Gordon equations on $ \mathbb{R}^{2}\times \mathbb{T} $

In this paper, for the small initial data in the suitably weighted Sobolev spaces on the product space $ \mathbb{R}^2\times\mathbb{T} $, we establish the global existence of smooth solutions to the 3-D quasilinear Klein-Gordon equations with quadratic nonlinearities. It is noted that the topic on the well-posedness of the nonlinear hyperbolic equations on product spaces arises from the studies for the propagation of waves along infinite homogeneous waveguides and the Kaluza-Klein theory. Our main result is based on the method of normal form including the parameters $ n\in\Bbb Z $ and the continuous induction method. In addition, the free profile of the solution is obtained by applying the weighted energy estimates and the temporal decay estimates.

A 5d perspective on the compactifications of 6d SCFTs to 4d mathcal{N} = 1 SCFTs

Compactifying 6d superconformal field theories (SCFTs) to 4d mathcal{N} = 1 theories on two-punctured spheres (tubes) and tori with flux is realized using duality domain walls in 5d mathcal{N} = 1 Kaluza-Klein (KK) theories, which are usually denoted by flux domain walls. We revisit this construction and study it in detail from the 5d perspective, specifically rephrasing it using the box graph description of the extended Coulomb branch phases of 5d theories. This perspective could be helpful in understanding how to equivalently realize the 4d mathcal{N} = 1 models from geometric engineering in M-theory. Along the way, we show how to recover various properties of the 4d theories from the 5d perspective, such as the flux associated to the domain wall configurations and the presence of a mathfrak{u} (1) global symmetry in the 4d theory descending from the KK symmetry on the tube, which is broken to a discrete subgroup on a flux torus. We demonstrate all of these ideas using the rank 1 E-string theory.

The early universe scenario in FRW and K-K models: A study

The early Universe has been a subject of research for many cosmologists and it is reviewed and analyzed rigorously in cosmology recently. Thermal history and theory of phase transition coordinate us to elucidate the evolution of the Universe at its early stages and is interesting to get a gist of early universe behavior. At phase transition, effective potential plays a significant role for the kinds of transition that occurred during the evolution.  The temperature, at which phase transition occurs, can be determined at minimum effective potential.  It is also known fact that temperature of the Universe has changed considerably with its evolution.  The present work investigates the time-temperature relation in four- dimensional and five-dimensional cosmological models.  A comparison of time- temperature relation in FRW model with that of Kaluza-Klein (K-K) model demonstrates that temperature decreases faster in Kaluza-Klein model. The investigation demonstrates the important role played by extra dimension in the study of time-temperature relation at the early Universe scenario.

Lower-dimensional limits of cubic Lovelock gravity

We obtain the lower-dimensional limits (p=2,3,4,5,6) of cubic Lovelock gravity through a regularized Kaluza-Klein reduction. By taking a flat internal space for simplicity, we also study the static black hole solutions in the resulting theories. We show that the solutions match with the ones obtained from the “naive limit” of D-dimensional equation for the metric function, which is obtained by first scaling the relevant couplings by a factor of 1D−p and then taking the limit D→p, with one important exception: In 4D, one obtains the expected solution only for the black hole with a planar horizon.

Quiver Symmetries and Wall-Crossing Invariance

We study the BPS particle spectrum of five-dimensional superconformal field theories on $$\mathbb {R}^4\times S^1$$ with one-dimensional Coulomb branch, by means of their associated BPS quivers. By viewing these theories as arising from the geometric engineering within M-theory, the quivers are naturally associated to the corresponding local Calabi–Yau threefold. We show that the symmetries of the quiver, descending from the symmetries of the Calabi–Yau geometry, together with the affine root lattice structure of the flavor charges, provide equations for the Kontsevich–Soibelman wall-crossing invariant. We solve these equations iteratively: the pattern arising from the solution is naturally extended to an exact conjectural expression, that we provide for the local Hirzebruch $$\mathbb {F}_0$$ , and local del Pezzo $$dP_3$$ and $$dP_5$$ geometries. Remarkably, the BPS spectrum consists of two copies of suitable 4d $$\mathcal {N}=2$$ spectra, augmented by Kaluza-Klein towers.

Kaluza–Klein reductions of maximally supersymmetric five-dimensional Lorentzian spacetimes

A recent study of filtered deformations of (graded subalgebras of) the minimal five-dimensional Poincaré superalgebra resulted in two classes of maximally supersymmetric spacetimes. One class are the well-known maximally supersymmetric backgrounds of minimal five-dimensional supergravity, whereas the other class does not seem to be related to supergravity. This paper is a study of the Kaluza–Klein (KK) reductions to four dimensions of this latter class of maximally supersymmetric spacetimes. We classify the Lorentzian and Riemannian KK reductions of these backgrounds, determine the fraction of the supersymmetry preserved under the reduction and in most cases determine explicitly the geometry of the four-dimensional quotient. Among the many supersymmetric quotients found, we highlight a number of novel non-homogeneous four-dimensional Lorentzian spacetimes admitting N = 1 supersymmetry, whose supersymmetry algebra is not a filtered deformation of any graded subalgebra of the four-dimensional N = 1 Poincaré superalgebra. Any of these four-dimensional Lorentzian spacetimes may serve as the arena for the construction of new rigidly supersymmetric field theories.

Comment on “PDM Klein–Gordon oscillators in cosmic string spacetime in magnetic and Aharonov–Bohm flux fields within the Kaluza–Klein theory”

We show that the spectra of some models with supposed physical utility derived recently are not correct. The eigenvalues to the radial differential equations do not satisfy well-known theorems. The origin of the problem is that those equations are not exactly solvable but conditionally solvable. Present analysis shows that the author overlooked a second condition that provides a relationship between the model parameters. Consequently, all the conclusions derived from those supposedly exact eigenvalues cannot be correct.

Cylinder quantum field theories at small coupling

We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential V is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential V and an infinite tower of free massive Kaluza-Klein (KK) modes. Moving slightly away from the deep IR region has the effect of switching on interactions between the zero mode and the KK modes, whose strength is controlled by powers of the coupling, hence making the interactions increasingly suppressed. We take the notable example of Liouville field theory and, starting from its worldline version, we compute the torus (one-loop) partition function perturbatively in the coupling constant. The partition function at leading order is invariant under a T-duality transformation that maps the radius of the cylinder to its inverse and rescales it by the square of the Schwinger parameter of the cylinder. We show that this behavior is a universal feature of cylinder QFTs.

Compatibility of the dimensional reduction and variation procedures for a quadratic curvature model with a Kaluza–Klein Ansatz

The introduction of extra dimensions is an invaluable strategy for the unification of gravity with other physical fields. Nevertheless, the matter in hand is to be eventually reduced to the actual 4D spacetime. The Kaluza-Klein theory is no exception to this well-known scheme. There are two procedures to obtain the field equations from a higher dimensional action. One can either take the variation of the effective action in that higher dimension and then reduce the resulting equations or reduce the higher dimensional action to the actual 4D and henceforward take the variations with respect to the constituent fields of the theory. Here, for the case of a quadratic curvature model with a Kaluza-Klein ansatz the field equations are obtained from the reduced action and compatibility of these two procedures is discussed in detail.

Gravity at the tip of the throat

We study the gravitational signatures that arise from compactifying Type IIB supergravity on a compact space containing a Klebanov-Strassler warped throat. After reviewing the dimensional reduction of the 10d graviton and explicitly obtaining the equa- tions of motion for the 4d tensor hμν, vector hμn and scalar hmn modes, we find the masses and wavefunctions of the Kaluza-Klein tower of spin-2 states. We explore how the masses and wavefunctions depend on the balance between the strength of the warping and the size of the bulk, and how these relate to the range and strength of the interactions which correct the Newtonian gravitational potential. By computing the modified Newtonian potential for sources on a brane somewhere along the throat, and applying consistency constraints on the Klebanov-Strassler parameters, we obtain predictions for the phenomenological pa- rameter space. In the case of a fully warped throat, and depending on where the brane is along the throat, these predictions are narrow in range and consistent with current obser- vational and experimental constraints. We also begin an exploration of gravitational wave signatures of KK gravitons in warped throats, finding that strong warping can bring the corresponding frequencies down to the windows of current and proposed experiments.

Conformally coupled theories and their deformed compact objects: From black holes, radiating spacetimes to eternal wormholes

We study a higher order conformally coupled scalar tensor theory endowed with a covariant geometric constraint relating the scalar curvature with the Gauss-Bonnet scalar. It is a particular Horndeski theory including a canonical kinetic term but without shift or parity symmetry for the scalar. The theory also stems from a Kaluza-Klein reduction of a well defined higher dimensional metric theory. Properties of an asymptotically flat spherically symmetric black hole are analyzed, and new slowly rotating and radiating extensions are found. Through disformal transformations of the static configurations, gravitating monopole-like solutions and eternal wormholes are presented. The latter are shown to extract from spacetime possible naked singularities, yielding completely regular and asymptotically flat spacetimes.