Multigravity in six dimensions: Generating bounces with flat positive tension branes

We present a generalization of the five dimensional multigravity models to six dimensions. The key characteristic of these constructions is that that we obtain solutions which do not have any negative tension branes while at the same time the branes are kept flat. This is due to the fact that in six dimensions the internal space is not trivial and its curvature allows bounce configurations with the above feature. These constructions give for the first time a theoretically and phenomenologically viable realization of multigravity.Comment: 27 pages, 13 figures, typos correcte

Zooplankton II. Macroplankton and Long-Term Series

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Addendum to: Modelling duality between bound and resonant meson spectra by means of free quantum motions on the de Sitter space-time dS

In the article under discussion the analysis of the spectra of the unflavored mesons lead us to some intriguing insights into the possible geometry of space-time outside the causal Minkowski light cone and into the nature of strong interactions. In applying the potential theory concept of geometrization of interactions, we showed that the meson masses are best described by a confining potential composed by the centrifugal barrier on the three-dimensional spherical space, $S^{3}$, and of a charge-dipole potential constructed from the Green function to the $S^{3}$ Laplacian. The dipole potential emerged in view of the fact that $S^{3}$ does not support single-charges without violation of the Gauss theorem and the superposition principle, thus providing a natural stage for the description of the general phenomenon of confined charge-neutral systems. However, in the original article we did not relate the charge-dipoles on $S^{3}$ to the color neutral mesons, and did not express the magnitude of the confining dipole potential in terms of the strong coupling $\alpha_{S}$ and the number of colors, $N_{c}$, the subject of the addendum. To the amount $S^{3}$ can be thought of as the unique closed space-like geodesic of a four-dimensional de Sitter space-time, $dS_{4}$, we hypothesized the space-like region outside the causal Einsteinian light cone (it describes virtual processes, among them interactions) as the $(1+4)$-dimensional subspace of the conformal $(2+4)$ space-time, foliated with $dS_{4}$ hyperboloids, and in this way assumed relevance of $dS_{4}$ special relativity for strong interaction processes. The potential designed in this way predicted meson spectra of conformal degeneracy patterns, and in accord with the experimental observations. We now extract the $\alpha_{s}$ values in the infrared from data on meson masses. The results obtained are compatible with the $\alpha_{s}$ estimates provided by other approaches

Modelling duality between bound and resonant meson spectra by means of free quantum motions on the de Sitter space-time dS4

The real parts of the complex squared energies defined by the resonance poles of the transfer matrix of the Pöschl-Teller barrier, are shown to equal the squared energies of the levels bound within the trigonometric Scarf well potential. By transforming these potentials into parts of the Laplacians describing free quantum motions on the mutually orthogonal open-time-like hyperbolic-, and closed-space-like spherical geodesics on the conformally invariant de Sitter space-time, dS4, the conformal symmetries of these interactions are revealed. On dS4 the potentials under consideration naturally relate to interactions within colorless two-body systems and to cusped Wilson loops. In effect, with the aid of the dS4 space-time as unifying geometry, a conformal symmetry based bijective correspondence (duality) between bound and resonant meson spectra is established at the quantum mechanics level and related to confinement understood as color charge neutrality. The correspondence allows to link the interpretation of mesons as resonance poles of a scattering matrix with their complementary description as states bound by an instantaneous quark interaction and to introduce a conformal symmetry based classification scheme of mesons. As examples representative of such a duality we organize in good agreement with data 71 of the reported light flavor mesons with masses below ∼ 2350 MeV into four conformal families of particles placed on linear f0, $\pi$ , $\eta$ , and a0 resonance trajectories, plotted on the ℓ/M plane. Upon extending the sec2 $\chi$ by a properly constructed conformal color dipole potential, shaped after a tangent function, we predict the masses of 12 “missing” mesons. We furthermore notice that the f0 and $\pi$ trajectories can be viewed as chiral partners, same as the $\eta$ and a0 trajectories, an indication that chiral symmetry for mesons is likely to be realized in terms of parity doubled conformal multiplets rather than, as usually assumed, only in terms of parity doubled single SO(3) states. We attribute the striking measured meson degeneracies to conformal symmetry dynamics within color neutral two-body systems, and conclude on the usefulness of the de Sitter space-time, dS4, as a tool for modelling strong interactions, on the one side, and on the relevance of hyperbolic and trigonometric potentials in constituent quark models of hadrons, on the other

Human health risk assessment for aluminium, aluminium oxide, and aluminium hydroxide.

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