Number Of Large Extra Dimensions Research Articles

Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks.

In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.

The Hawking effect and the bounds on greybody factor for higher dimensional Schwarzschild black holes

In this work, we have considered a n-dimensional Schwarzschild–Tangherlini black hole spacetime with massless minimally coupled free scalar fields in its bulk and 3-brane. The bulk scalar field equation is separable using the higher dimensional spherical harmonics on (n-2)-sphere. First, using the Hamiltonian formulation with the help of the recently introduced near-null coordinates we have obtained the expected temperature of the Hawking effect, identical for both bulk and brane localized scalar fields. Second, it is known that the spectrum of the Hawking effect as seen at asymptotic future does not correspond to a perfect black body and it is properly represented by a greybody distribution. We have calculated the bounds on this greybody factor for the scalar field in both bulk and 3-brane. Furthermore, we have reaffirmed that these bounds predict a decrease in the greybody factor as the spacetime dimensionality n increases and also reaffirmed that for a large number of extra dimensions the Hawking quanta is mostly emitted in the brane.

Hawking radiation spectra for scalar fields by a higher-dimensional Schwarzschild–de Sitter black hole

In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de-Sitter black hole as well as on the projected-on-the-brane 4-dimensional background. The scalar fields have also a non-minimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then proceed to derive the Hawking radiation spectra for a higher-dimensional Schwarzschild-de-Sitter black hole, and we study both bulk and brane channels. We demonstrate that the non-minimal field coupling, that creates an effective mass term for the fields, suppresses the energy emission rates while the cosmological constant assumes a dual role. By computing the relative energy rates and the total emissivity ratio for bulk and brane emission, we demonstrate that the combined effect of a large number of extra dimensions and value of the field coupling gives to the bulk channel the clear domination in the bulk-brane energy balance.

Extra-dimensional curvature suppression of the effective four-dimensional vacuum energy density

Considering a very large number of extra dimensions, N → ∞, we show that in the effective four-dimensional picture, to leading order in N, both the cosmological constant in N + 4 dimensions and the curvature of the extra dimensions (curved as spheres) give the same type of contributions. Furthermore, in this limit, the extra-dimensional curvature naturally suppresses the effect of a positive cosmological constant, so that the resulting effective potential governing the vacuum energy in the effective 4 − D picture has a leading 1/N dependence (i.e. vanishing in the large N limit). We can understand qualitatively this effect in a heuristic picture by thinking that both visible and extra dimensions have an equal sharing of the curvature caused by Λ. In this case when increasing the overall number of dimensions by adding N extra dimensions, then if N is large, the visible dimensions do not have to curve too much; hence, a small four-dimensional vacuum energy follows. In the large N picture, the potential can also be stabilized by a small (i.e. vanishing at large N) expectation value of a four-index field strength.

Kaluza-Klein theory in the limit of large number of extra dimensions

The Kaluza-Klein compactification in the limit of a large number of extra dimensions is studied. The starting point is the Einstein-Hilbert action plus cosmological constant in $4+\mathbf{D}$ dimensions. It is shown that in the large $\mathbf{D}$ limit the effective four-dimensional cosmological constant is of order $1/\mathbf{D}$, whereas the size of the extra dimensions remains finite. A 't Hooft-like large $\mathbf{D}$ expansion of the effective Lagrangian for the Kaluza-Klein scalar and gauge fields arising from the dimensional reduction is considered. It is shown that the propagator of the scalar field associated to the determinant of the metric of the extra dimensions is strongly suppressed. This is an interesting result as in standard Kaluza-Klein theory this scalar degree of freedom is responsible for the constraint on the gauge fields which makes it impossible to recover the usual Yang-Mills equations. Moreover in the large $\mathbf{D}$ limit it turns out that the ultraviolet divergences due to the interactions between gauge and scalar fields are softened.

Extra dimensions at the CERN LHC via mini-black holes: Effective Kerr-Newman brane-world effects

We solve Einstein equations on the brane to derive the exact form of the brane-world-corrected perturbations in Kerr-Newman singularities, using Randall-Sundrum and Arkani-Hamed-Dimopoulos-Dvali (ADD) models. It is a consequence of such models that Kerr-Newman mini-black holes can be produced in LHC. We use this approach to derive a normalized correction for the Schwarzschild Myers-Perry radius of a static $(4+n)$-dimensional mini-black hole, using more realistic approaches arising from Kerr-Newman mini-black hole analysis. Besides, we prove that there are four Kerr-Newman black hole horizons in the brane-world scenario we use, although only the outer horizon is relevant in the physical measurable processes. Parton cross sections in LHC and Hawking temperature are also investigated as functions of Planck mass (in the LHC range 1--10 TeV), mini-black hole mass, and the number of large extra dimensions in brane-world large extra-dimensional scenarios. In this case a more realistic brane-effect-corrected formalism can achieve more precisely the effective extra-dimensional Planck mass and the number of large extra dimensions---in the Arkani-Hamed-Dimopoulos-Dvali model---or the size of the warped extra dimension---in Randall-Sundrum formalism.

Bounds on low scale gravity from RICE data and cosmogenic neutrino flux models

We explore limits on low scale gravity models set by results from the Radio Ice Cherenkov Experiment's (RICE) ongoing search for cosmic ray neutrinos in the cosmogenic, or GZK, energy range. The bound on MD, the fundamental scale of gravity, depends upon cosmogenic flux model, black hole formation and decay treatments, inclusion of graviton mediated elastic neutrino processes, and the number of large extra dimensions, d. Assuming proton-based cosmogenic flux models that cover a broad range of flux possibilities, we find bounds in the interval 0.9 TeV<MD<10 TeV. Heavy nucleus-based models generally lead to smaller fluxes and correspondingly weaker bounds. Values d=5, 6 and 7, for which laboratory and astrophysical bounds on LSG models are less restrictive, lead to essentially the same limits on MD.

Cosmic ray signals from mini black holes in models with extra dimensions: an analytical/Monte Carlo study

We present a study of the multiplicities, of the lateral distributions and of the ratio of the electromagnetic to the hadronic components in the air showers, generated by the collision in the atmosphere of an incoming high energy cosmic ray and mediated by the formation of a mini black hole, predicted in TeV scale gravity models with large extra dimensions. The analysis is performed via a large scale simulation of the resulting cascades over the entire range ($10^{15}-10^{19}$eV) of ultra high initial energies, for several values of the number of large extra dimensions, for a variety of altitudes of the initial interaction and with the energy losses in the bulk taken into account. The results are compared with a representative of the standard events, namely the shower due to the collision of a primary proton with a nucleon in the atmosphere. Both the multiplicities and the lateral distribution of the showers show important differences between the two cases and, consequently, may be useful for the observational characterization of the events. The electromagnetic/hadronic ratio is strongly fluctuating and, thus, less decisive for the altitudes considered.

Submillimeter tests of the gravitational inverse-square law

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R <= 160 microns, and on two equal-sized large extra dimensions of R <= 130 microns. Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of pseudoscalars with m <= 10 meV/c^2.

Fractional dynamics, Cantorian space–time and the gauge hierarchy problem

The gauge hierarchy problem in particle physics refers to the large numerical disparity between the value of the Planck mass (MPl≃1.22×1019 GeV) and the mass scale of the electroweak interaction (MEW≈102 GeV). Explaining the hierarchy paradox has been attempted so far in quantum field models based on supersymmetry or higher dimensional space–time with a large number of extra dimensions (brane theories). Despite several years of experimental search, there is currently no validation for either one of these models. We approach the hierarchy paradox using the methodology of fractal operators in four-dimensional space–time. It is found that departure from the inverse-square gravity in the high-energy regime emerges naturally from the fractional Helmholtz equation and offers a simple resolution to the problem. Our work makes an explicit connection between the hierarchy problem and Cantorian geometry of space–time on energy scales comparable to the Planck mass.

Bhabha scattering with radiated gravitons at linear colliders

We study the process e+- e- -> e+- e- +- missing energy at a high-energy e+- e- collider, where the missing energy arises from the radiation of Kaluza-Klein gravitons in a model with large extra dimensions. It is shown that at a high-energy linear collider, this process can not only confirm the signature of such theories but can also sometimes be comparable in effectiveness to the commonly discussed channel e+- e- -> gamma +- missing energy, especially for a large number of extra dimensions and with polarized beams. We also suggest some ways of distinguishing the signals of a graviton tower from other types of new physics signals by combining data on our suggested channel with those on the photon-graviton channel.

Contact interactions in D-brane models

We compute the tree-level four-point scattering amplitudes in string models where matter fields live on D-brane intersections. Extracting the contribution of massless modes, we are left with dimension-six four-fermion operators which in general receive contributions from three different sources: exchange of massive Kaluza--Klein excitations, winding modes and string oscillator states. We compute their coefficients and extract new bounds on the string scale in the brane-world scenario. This is contrasted with the situation where matter fields arise from open strings with both ends confined on the same collection of D-branes, in which case the exchange of massive string modes leads to dimension-eight operators that have been studied in the past. When matter fields live on brane intersections, the presence of dimension-six operators increases the lower bound on the string scale to 2--3 TeV, independently of the number of large extra dimensions.