De Sitter Special Relativity as a Possible Reason for Conformal Symmetry and Confinement in QCD

Abstract

Conformal symmetry and color confinement in the infrared regime of QCD are attributed to the global properties of a 4D space-time of a deSitter dS4 geometry which, according to the principle of deSitter special relativity, is viable outside the causal Minkowski light cone, where it reigns over the interactions involving the virtual gluon- and quark degrees of freedom of hadrons. Within this scenario, the conformal symmetry of QCD is a direct consequence of the conformal symmetry of the dS4 space- time, while the color confinement appears as a consequence of the innate charge neutrality of the unique closed space-like geodesic on this space, the three dimensional hypersphere S3, also being the unique dS4 sub-manifold suited as a stage for near rest-frame physics. In further making use of the principles of the mathematical discipline of potential theory, and postulating that fundamental interactions are defined by Green functions of Laplace operators on manifolds, taken here as the dS4 geodesics, a color-dipole potential has been derived on S3 whose magnitude, N_c\alpha_s is the product of the number of colors, N_c, and the strong coupling constant $\alpha_s$ in QCD, and pretty much as the amplitude, Z\alpha, of the Coulomb interaction following from QED. Hadrons now present themselves as light quarkish color-anticolor "dumbbells" in free 4D rotations around their mass centers, equivalent to inertial quantum motions along S3, possibly slightly perturbed by the color-dipole potential from above, attributed to a 4D gluon--anti-gluon "dumbbell" , sufficiently heavy to remain static to a good approximation. A description of the spectra of the unflavored mesons within the above scenario allows to extract the \alpha_s/\pi , value, which we obtain to vary between 0.58 and 0.8, and in accord with data extracted from the spin structure function.