Compact Extra Dimensions Research Articles

Brane compactifications and 4-dimensional geometry in the IKKT model

We study in detail certain brane solutions with compact extra dimensions M4×K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R6. We focus on the compactification moduli and the fluctuations of K⊂R6 and their physical significance. Mediated by the Poisson tensor, they contribute to the effective 4-dimensional metric on the brane, and thereby become gravitational degrees of freedom. We show that the zero modes corresponding to the global symmetries of the model lead to Ricci-flat 4-dimensional metric perturbations, wherever the energy–momentum tensor vanishes. Their coupling to the energy–momentum tensor depends on the extrinsic curvature of the brane.

Can dark energy emerge from quantum effects in a compact extra dimension?

The origin of the observed acceleration of the expansion of the universe is a major problem of modern cosmology and theoretical physics. Simple estimations of the contribution of vacuum to the density energy of the universe in quantum field theory are known to lead to catastrophic large values compared to observations. Such a contribution is therefore generally not regarded as a viable source for the acceleration of the expansion. In this letter we propose that the vacuum contribution actually provides a small positive value to the density energy of the universe. The underlying mechanism is a manifestation of the quantum nature of the gravitational field, through a Casimir-like effect from an additional compact dimension of space. A key ingredient is to assume that only modes with wavelength shorter than the Hubble length contribute to the vacuum. Such a contribution gives a positive energy density, has a Lorentz invariant equation of state in the usual 4D spacetime and hence can be interpreted as a cosmological constant. Its value agrees with observations for a radius of a 5th extra dimension given by $35\,\mu$m. This implies a modification of the gravitational inverse square law around this scale, close but below existing limits from experiments testing gravity at short range.

Heterotic mini-landscape in blow-up

Abstract Localization properties of fields in compact extra dimensions are crucial ingredients for string model building, particularly in the framework of orbifold compactifications. Realistic models often require a slight deviation from the orbifold point, that can be analyzed using field theoretic methods considering (singlet) fields with nontrivial vacuum expectation values. Some of these fields correspond to blow-up modes that represent the resolution of orbifold singularities. Improving on previous analyses we give here an explicit example of the blow-up of a model from the heterotic Mini-landscape. An exact identification of the blow-up modes at various fixed points and fixed tori with orbifold twisted fields is given. We match the massless spectra and identify the blow-up modes as non-universal axions of compactified string theory. We stress the important role of the Green-Schwarz anomaly polynomial for the description of the resolution of orbifold singularities.

More on divergences in brane world models

In this paper a model in a space-time with compact extra dimension is presented, describing five-dimensional fermion fields interacting with an electromagnetic field localized on a brane. This model can be considered as a toy model for examining possible consequences of the localization of gauge fields on a brane. It is shown that in the limit of infinite extra dimension, the lowest-order amplitudes of some processes in the resulting four-dimensional effective theory are divergent. Such a ``localization catastrophe'' can be inherent to more realistic brane world models with infinite extra dimensions.

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization of multiple zeta function with one arbitrary exponent. We find a limit on the scale dimension like \(\delta>\frac{1}{2}\) to keep the negative sign of the renormalized Casimir energy which is the difference between the regularized energy for two parallel plates and the one with no plates. We derive and calculate the Casimir force relating to the influence from the fractal additional compactified dimension between the parallel plates. The larger scale dimension leads to the greater revision on the original Casimir force. The two kinds of curves of Casimir force in the case of integer-numbered extra compactified dimension or fractal one are not superposition, which means that the Casimir force show whether the dimensionality of additional compactified space is integer or fraction.

Unwinding inflation

Higher-form flux that extends in all 3+1 dimensions of spacetime is a source of positive vacuum energy that can drive meta-stable eternal inflation. If the flux also threads compact extra dimensions, the spontaneous nucleation of a bubble of brane charged under the flux can trigger a classical cascade that steadily unwinds many units of flux, gradually decreasing the vacuum energy while inflating the bubble, until the cascade ends in the self-annihilation of the brane into radiation.With an initial number of flux quanta Q0≳N, this can result in N efolds of inflationary expansion while producing a scale-invariant spectrum of adiabatic density perturbations with amplitude and tilt consistent with observation. The power spectrum has an oscillatory component that does not decay away during inflation, relatively large tensor power, and interesting non-Gaussianities.Unwinding inflation fits naturally into the string landscape, and our preliminary conclusion is that consistency with observation can be attained without fine-tuning the string parameters. The initial conditions necessary for the unwinding phase are produced automatically by bubble formation, so long as the critical radius of the bubble is smaller than at least one of the compact dimensions threaded by flux.

Indirect dark matter search with the ANTARES neutrino telescope

Using the ANTARES neutrino telescope, the largest neutrino telescope in the Northern hemisphere, from its first configuration with 5 lines of photodetectors to the actual nominal one corresponding to a total of 12 lines, we have studied our ability to search indirectly an evidence of Dark Matter annihilations in heavy astrophysical objects as the Sun. First limits have been obtained using the data recorded by ANTARES in 2007 and 2008, and compared with neutrino fluxes predicted within a minimal supersymmetric extension of the Standard Model with supersymmetry-breaking scalar and gaugino masses constrained to be universal at the GUT scale, the CMSSM, as well as a minimal Universal Extra-Dimensions scenario with one extra compact dimension where all the Standard Model fields propagate into the bulk, the mUED. The current limits over the neutrino/muon fluxes coming from the dark matter self-annihilations, as well as the spin-dependent and spin-independent cross-sections, are presented.

Spectra of Hydrogen Atom with GUP and Extra Dimensions

We argue that the Generalized Uncertainty Ptinciple (GUP) and the compact Extra dimensions will lead the hydrogen atom has the non bounded state spectra which equal the free particle in extra dimensions. We use Generalized Uncertainty Principle (GUP) to calculate the new energy spectra of hydrogen atom, and which lives in three dimensional Euclidean spaces with one extra dimension. The result is not familiar with our known before that En =0 when n is large enough. In our modified new spectra, we obtain that En,ι,0 = (1+2βι2／ρ2) ι2／2mρ2, which is lager than zero. These new spectra give us new method to obtain the existence of extra dimensions. Finally, we find that the spectra are same as part of extra dimensions in planck scale.

Extra Dimensions Corrections for Fermionic Casimir Effect in Three Dimensional Box

We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field confined inside a three-dimensional rectangular box with one compact extra-dimension. We use the MIT bag model boundary condition for the confinement and M4 × S1 as the background spacetime. We use the direct mode summation method along with the Abel-Plana formula to compute the Casimir energy. We show analytically the extra-dimension corrections to the Fermionic Casimir effect to forward a new method of exploring the existence of the extra dimensions of the universe.

Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy

Euclidean embedding of the 11-dimensional M-theory turned out to require a very large space leaving lavish amounts of 242 dimensional pseudo truly empty “regions” devoid of space and time and consequently of anything resembling ordinary physical energy density. It is shown here using Nash embedding that the ratio of “solid” M-theory spacetime to its required embedding “non-spacetime” is 1/22 for a classical theory and 1/22.18033989 for an analogous fractal theory. This then leads to a maximal ordinary energy density equation equal to that of Einstein’s famous formula E=mc2 but multiplied with in full agreement with previous results obtained using relatively more conventional methods including running the electromagnetic fine structure constant in the exact solution of the hydrogen atom. Consequently, the new equation corresponds to a quantum relativity theory which unlike Einstein’s original equation gives quantitative predictions which agree perfectly with the cosmological measurements of WMAP and the analysis of certain supernova events. Never the less in our view dark energy also exists being the energy of the quantum wave amounting to 95.5 present of the total Einstein theoretical energy which is blind to any distinction between ordinary energy of the quantum particle and the dark energy of the quantum wave. However, since measurement leads to the collapse of the Hawking-Hartle quantum wave, dark energy being a quantum wave non-ordinary energy could not possibly be measured in the usual way unless highly refined quantum wave non-demolition technology is developed if possible. It is a further reason that dark energy having a different sign to ordinary energy is the cause behind the anti gravity force which is pushing the universe apart and accelerating cosmic expansion. Consequently it can be seen as the result of anticlastic Cartan-like curvature caused by extra compactified dimensions of spacetime. A simple toy model demonstration of the effect of curvature in a “material” space is briefly discussed.

Origin of family symmetries

AbstractDiscrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.

Q-form fields on p-branes

In this paper, we give one general method for localizing any form (q-form) field on p-branes with one extra dimension, and apply it to some typical p-brane models. It is found that, for the thin and thick Minkowski branes with an infinite extra dimension, the zero mode of the q-form fields with q<(p-1)/2 can be localized on the branes. For the thick Minkowski p-branes with one finite extra dimension, the localizable q-form fields are those with q<p/2, and there are also some massive bound Kaluza-Klein modes for these q-form fields on the branes. For the same q-form field, the number of the bound Kaluza-Klein modes (but except the scalar field (q=0)) increases with the dimension of the p-branes. Moreover, on the same p-brane, the q-form fields with higher q have less number of massive bound KK modes. While for a family of pure geometrical thick p-branes with a compact extra dimension, the q-form fields with q<p/2 always have a localized zero mode. For a special pure geometrical thick p-brane, there also exist some massive bound KK modes of the q-form fields with q<p/2, whose number increases with the dimension of the p-brane.

HOLOGRAPHIC SPACETIME

The theory of holographic spacetime (HST) generalizes both string theory and quantum field theory (QFT). It provides a geometric rationale for supersymmetry (SUSY) and a formalism in which super-Poincare invariance follows from Poincare invariance. HST unifies particles and black holes, realizing both as excitations of noncommutative geometrical variables on a holographic screen. Compact extra dimensions are interpreted as finite-dimensional unitary representations of super-algebras, and have no moduli. Full field theoretic Fock spaces, and continuous moduli are both emergent phenomena of super-Poincare invariant limits in which the number of holographic degrees of freedom goes to infinity. Finite radius de Sitter (dS) spaces have no moduli, and break SUSY with a gravitino mass scaling like Λ1/4. In regimes where the Covariant Entropy Bound is saturated, QFT is not a good description in HST, and inflation is such a regime. Following ideas of Jacobson, the gravitational and inflaton fields are emergent classical variables, describing the geometry of an underlying HST model, rather than "fields associated with a microscopic string theory". The phrase in quotes is meaningless in the HST formalism, except in asymptotically flat and AdS spacetimes, and some relatives of these.

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension δ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.

Flux vacua in DBI type Einstein–Maxwell theory

We study compactification of extra dimensions in a theory of Dirac–Born–Infeld type gravity. We investigate the solution for Minkowski spacetime with an S 2 extra space as well as that for de Sitter spacetime (S 4) with an S 2 extra space. They are derived by the effective potential method in the presence of the magnetic flux on the extra sphere. We also consider the higher-dimensional generalization of the solutions. We find that, in a certain model, the radius of the extra space has a minimum value independent of the higher-dimensional Newton constant.

Light scalars in strongly-coupled extra-dimensional theories

The low-energy dynamics of five-dimensional Yang-Mills theories compactified on S^1 can be described by a four-dimensional gauge theory coupled to a scalar field in the adjoint representation of the gauge group. Perturbative calculations suggest that the mass of this elementary scalar field is protected against power divergences, and is controlled by the size of the extra dimension R. As a first step in the study of this phenomenon beyond perturbation theory, we investigate the phase diagram of a SU(2) Yang-Mills theory in five dimensions regularized on anisotropic lattices and we determine the ratios of the relevant physical scales. The lattice system shows a dimensionally reduced phase where the four-dimensional correlation length is much larger than the size of the extra dimension, but still smaller than the four-dimensional volume. In this region of the bare parameter space, at energies below 1/R, the non-perturbative spectrum contains a \emph{light} scalar state. This state has a mass that is independent of the cut-off, and a small overlap with glueball operators. Our results suggest that light scalar fields can be introduced in a lattice theory using compactified extra dimensions, rather than fine tuning the bare mass parameter.

Cosmological wormholes in Lovelock gravity

We present dynamic wormhole solutions in the framework of Lovelock gravity with compact extra dimensions. Calculations are done in $D=7$, although they can be extended to an arbitrary number of extra dimensions. It is shown that as the wormhole inflates with the three-dimensional space, the extra dimensions deflate to very small, yet nonvanishing scales. The weak energy condition is shown to hold for certain ranges of the free parameters, everywhere, down to the throat of the wormhole.

Constraint on compactification scale via recently observed baryonic Λ b → Λℓ + ℓ − channel and analysis of the Σ b → Σℓ + ℓ − transition in SM and UED scenario

We obtain a lower limit on the compactification scale of extra dimension via comparison of the branching ratio in the baryonic $\Lambda_b\rightarrow \Lambda \mu^+ \mu^-$ decay channel recently measured by CDF collaboration and our previous theoretical study. We also use the newly available form factors calculated via light cone QCD sum rules in full theory to analyze the flavour changing neutral current process of the $\Sigma_b \rightarrow \Sigma \ell^+ \ell^-$ in universal extra dimension scenario in the presence of a single extra compact dimension. We calculate various physical quantities like branching ratio, forward-backward asymmetry, baryon polarizations and double lepton polarization asymmetries defining the decay channel under consideration. We also compare the obtained predictions with those of the standard model.

D-branes from classical macroscopic strings

This paper is a sequel to the series of papers dedicated to model independent analysis of brane-like extended objects in curved backgrounds. In particular, we study cylindrical membranes wrapped around the extra compact dimension of a (D + 1)-dimensional Riemann–Cartan spacetime. The world-sheet equations are obtained from the universally valid conservation equations of the membrane stress–energy and spin tensors. In the limit of small extra dimension, the dimensionally reduced theory is obtained. The narrow membrane becomes an effective string characterized not only by tension and spin, but also by electric and dilaton charges. The boundary of such an effective string has been shown to live in less spacetime dimensions than its interior. Precisely, the string endpoints are trapped by the surfaces orthogonal to the gradient of the effective dilaton field. The string dynamics has been shown to follow from an action functional subject to the Dirichlet boundary conditions. This way, we have succeeded in obtaining a macroscopic D-brane analogue.

Asymptotic latent solitons, black strings, and black branes inf(R)gravity

We investigate nonlinear $f(R)$ theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A pointlike matter source has the dustlike equation of state in our three dimensions and nonzero equations of state in the extra dimensions. We obtain solutions of linearized Einstein equations with this matter source taking into account effects of nonlinearity of the model. There are two asymptotic regions where solutions satisfy the gravitational tests at the same level of accuracy as general relativity. According to these asymptotic regions, there are two classes of solutions. We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known result of the linear theory. The asymptotic black strings and black branes are particular cases of these asymptotic solutions. The second class of asymptotic solitons exists only in multidimensional nonlinear models. The main feature for both of these classes of solutions is that the matter sources have tension in the extra dimensions.