Space-like Dimensions Research Articles

Bianchi identities in higher dimensions

A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension n. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in n − 4 spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers–Perry metric as an explicit example of a vacuum type D spacetime to show that principal geodesic null congruences in vacuum type D spacetimes do not share this property.

The membrane as a perturbation around string-like configurations

The bosonic membrane in a partial gauge, where one space dimension is eliminated, is formulated as a perturbation theory around an exact free string-like solution. This perturbative regime corresponds to a situation where one of the world-volume space-like dimensions is much greater than the other, so that the membrane has the form of a narrow band or large hoop with string excitations being transverse to the widest dimension. The perturbative equations of motion are studied and solved to first order. Furthermore, for the open or semi-open cases and to any order in perturbation theory, we construct a canonical transformation that will transform the membrane Hamiltonian into a free string-like Hamiltonian and a boundary Hamiltonian. Thus the membrane dynamics in our perturbation scheme is essentially captured by an interacting boundary theory defined on a two-dimensional world-sheet. A possible implication of this to M-theory is discussed.

Bouncing braneworlds

We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commences its expansion from a quasi-singular state during which both the Hubble parameter and the energy density and pressure remain finite while the curvature tensor diverges. The non-singular and quasi-singular behaviour which we have discovered differs both qualitatively and quantitatively from what is usually observed in braneworld models with spacelike extra dimensions and could have interesting cosmological implications.

Cosmological constraints on bulk neutrinos.

Recent models invoking extra space-like dimensions inhabited by (bulk) neutrinos are shown to have significant cosmological effects if the size of the largest extra dimension is R greater, similar 1 fm. We consider effects on cosmic microwave background anisotropies, big bang nucleosynthesis, deuterium and 6Li photoproduction, diffuse photon backgrounds, and structure formation. The resulting constraints can be stronger than either bulk graviton overproduction constraints or laboratory constraints.

Closed system of equations on a brane

We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations obtained. We consider bulk spaces with both spacelike and timelike extra dimension, with and without the Z 2 symmetry of reflection relative to the brane.

Tevatron—probing TeV-scale gravity today

The production of black holes at Tevatron and LHC in spacetimes with compactified space-like large extra dimensions is studied. Either black holes can already be observed in p̄p collisions at √s = 1.8 TeV or the fundamental gravity scale has to be above 1.4 TeV. At LHC the creation of a large number of quasi-stable black holes is predicted, with lifetimes beyond several hundred fm/c.A cut-off in the high-PT jet cross section is shown to be a unique signature of black hole production. This signal is compared to the jet plus missing energy signature due to graviton production in the final state as proposed by the ATLAS collaboration.

Froissart-martin bound in spaces of compact dimensions

By considering the example of five-dimensional spacetime, it is shown that the presence of extra spacelike compact dimensions (in addition to common Minkowski space) does not lead to any changes in the prerequisites for proving the Froissart-Martin bound.

A GEOMETRIC BASIS FOR THE STANDARD-MODEL GAUGE GROUP

A geometric approach to the standard model in terms of the Clifford algebra Cℓ7 is advanced. The gauge symmetries and charge assignments of the fundamental fermions and the higgs boson arise uniquely from a geometric model involving only four extra space-like dimensions. A key feature of the model is its use of double-sided operations on the algebraic spinors. The four added dimensions form a natural basis for the Higgs isodoublet field.

A geometric basis for the standard-model gauge group

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided (exterior) and right-sided (interior) types. By definition, Poincare transformations are exterior ones. We consider all rotations in the seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincare group and form the group SU(2)_L, interior ones that constitute SU(3)_C, and a unique group of coupled double-sided rotations with U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and isotopic symmetries within the restrictions of the Coleman--Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU(2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.

Time-like extra dimension and cosmological constant in brane models

We discuss the general models with one time-like extra dimension and parallel 3-branes on the space–time M 4× M 1. We also construct the general brane models or networks with n space-like and m time-like extra dimensions and with constant bulk cosmological constant on the space–time M 4×( M 1) n+ m , and point out that there exist two kinds of models with zero bulk cosmological constant: for static solutions, we have to introduce time-like and space-like extra dimensions, and for non-static solutions, we can obtain the models with only space-like extra dimension(s). In addition, we give two simplest models explicitly, and comment on the 4-dimensional effective cosmological constant.

Magnetogenesis and the dynamics of internal dimensions

The dynamical evolution of internal space-like dimensions breaks the invariance of the Maxwell's equations under Weyl rescaling of the (conformally flat) four-dimensional metric. Depending upon the number and upon the dynamics of internal dimensions large scale magnetic fields can be created. The requirements coming from magnetogenesis together with the other cosmological constraints are examined under the assumption that the internal dimensions either grow or shrink (in conformal time) prior to a radiation dominated epoch. If the internal dimensions are growing the magnitude of the generated magnetic fields can seed the galactic dynamo mechanism.

Mass hierarchy and localization of gravity in extra time

We consider Randall–Sundrum model with localized gravity, replacing the extra compact space-like dimension by a time-like one. In this way the solution to the hierarchy problem can be reconciled with a correct cosmological expansion of the visible universe, just as a trivial result of the sign flip of cosmological constants in the bulk and on the 3-branes relative to the case of extra space-like dimension. Some phenomenological aspects of the proposed scenario related to the tachyonic nature of Kaluza–Klein states of graviton are also discussed.

Domain walls and dimensional reduction

We study some properties of a dimensional reduction mechanism for fermions in an odd number D+1 of space-time dimensions. A fermionic field is equipped with a mass term with domain-wall-like defects along one of the space-like dimensions, which is moreover compactified. We show that there is a regime such that the only relevant degrees of freedom are massless fermionic fields in D dimensions. For any fixed gauge field configuration, the extra modes may be decoupled, since they can be made arbitrarily heavy. This decoupling combines the usual Kaluza–Klein one, due to the compactification, with a mass enhancement for the non-zero-modes provided by the domain wall mechanism. We obtain quantitative results on the contribution of the massive modes in the cases D=2 and D=4.

Cosmological 3-brane solutions

We analyze cosmological equations in the brane world scenario with one extra space-like dimension. We demonstrate that the cosmological equations can be reduced to the usual 4D Friedmann type if the bulk energy-momentum tensor is different from zero. We then generalize these equations to the case of a brane of finite thickness. We also demonstrate that when the bulk energy-momentum tensor is different from zero, the extra space-like dimension can be compactified with a single brane and show that the stability of the radius of compactification implies standard cosmology and vice versa. For a brane of finite thickness, we provide a solution such that the 4D Planck scale is related to the fundamental scale by the thickness of the brane. In this case, compactification of the extra dimension is unnecessary.

Conformal symmetry and duality between free particle, H atom, and harmonic oscillator

We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given as the lightcone momentum of an additional dimension. The duality is in the sense that the classical action of these systems are gauge fixed forms of the same worldline gauge theory action at the classical level, and they are all described by the same unitary representation of the conformal group SO(d,2) at the quantum level. The worldline action has a gauge symmetry Sp(2) which treats canonical variables (x,p) as doublets and exists only with a target spacetime that has d spacelike dimensions and two timelike dimensions. This spacetime is constrained due to the gauge symmetry, and the various dual solutions correspond to solutions of the constraints with different topologies. For example, for the H-atom the two timelike dimensions X^{0'},X^{0} live on a circle. The model provides an example of how realistic physics can be viewed as existing in a larger covariant space that includes two timelike coordinates, and how the covariance in the larger space unifies different looking physics into a single system.

Center vortices and confinement versus screening

We study adjoint and fundamental Wilson loops in the center-vortex picture of confinement, for gauge group SU(N) with general N. There are N-1 distinct vortices, whose properties, including collective coordinates and actions, we study. In d=2 we construct a center-vortex model by hand so that it has a smooth large-N limit of fundamental-representation Wilson loops and find, as expected, confinement. Extending an earlier work by the author, we construct the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion in powers of $\rho/M^2$, where $\rho$ is the vortex density per unit area and M is the vortex inverse size, and find, as expected, screening. The leading term of the adjoint potential shows a roughly linear regime followed by string breaking when the potential energy is about 2M. This leading potential is a universal (N-independent at fixed fundamental string tension $K_F$) of the form $(K_F/M)U(MR)$, where R is the spacelike dimension of a rectangular Wilson loop. The linear-regime slope is not necessarily related to $K_F$ by Casimir scaling. We show that in d=2 the dilute vortex model is essentially equivalent to true d=2 QCD, but that this is not so for adjoint representations; arguments to the contrary are based on illegal cumulant expansions which fail to represent the necessary periodicity of the Wilson loop in the vortex flux. Most of our arguments are expected to hold in d=3,4 also.

Instanton effects in string cosmology

We consider the gauge dyonic string solution of the K3 compactified heterotic string theory in a four-dimensional cosmological context. Since for this solution Green-Schwarz as well as Chern-Simons corrections have been taken into account it contains both world-sheet and string loop corrections. The cosmological picture is obtained by rotating the world-volume of the gauge dyonic string into two space-like dimensions and compactifying those dimensions on a two torus. We compare the result with gauge neutral extreme and non-extreme cosmologies and find that the non-trivial Yang-Mills background leads to a solution without any singularities whereas for trivial Yang-Mills backgrounds some of the fields become always singular at the big bang.

Bubbles in Kaluza-Klein theories with spacelike or timelike internal dimensions

Bubbles are pointlike regular solutions of the higher-dimensional Kaluza-Klein equations that appear as naked singularities in four dimensions. We analyze all such possible solutions in five-dimensional (5D) Kaluza-Klein theory that are static and spherically symmetric. We show that they can be obtained by taking unusual choices of the parameters in the dyonic black hole solutions, and find that regularity can only be achieved if their electric charge is zero. However, they can be neutral or possess magnetic charge. We study some of their properties, both in theories where the internal dimension is spacelike as well as timelike. Since bubbles do not have horizons, they have no entropy, nor do they emit any thermal radiation, but they are, in general, nonextremal objects. In the two-timing case, it is remarkable that nonsingular massless monopoles are possible, probably signaling a new pathology of these theories. These two-timing monopoles connect two asymptotically flat regions, and matter can flow from one region to the other. We also present a $C$-type solution that describes neutral bubbles in uniform acceleration, and we use it to construct an instanton that mediates the breaking of a cosmic string by forming bubbles at its ends. The rate for this process is also calculated. Finally, we argue that a similar solution can be constructed for magnetic bubbles, and that it can be used to describe a semiclassical instability of the two-timing vacuum against production of massless monopole pairs.

Generalization of the Coleman–Mandula theorem to higher dimension

The Coleman–Mandula theorem, which states that space–time and internal symmetries cannot be combined in any but a trivial way, is generalized to an arbitrarily higher spacelike dimension. Prospects for further generalizations of the theorem (spacelike representations, larger timelike dimension, infinite number of particle types) are also discussed. The original proof relied heavily on the Dirac formalism, which was not well defined mathematically at that time. The proof given here is based on the rigorous version of the Dirac formalism, based on the theory of distributions. This work also serves to demonstrate the suitability of this formalism for practical applications.

The embedding of General Relativity in five dimensions

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbell's procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.