Color confinement at the boundary of the conformally compactified ${\mathrm{AdS}}_5$

Abstract

The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of ${\mathrm{AdS}}_5$ spacetime, topologically equivalent to the closed manifold $S^1\times S^3$, by considering the coupling of two massless opposite charges on it. Taking the interaction potential as the analog of Coulomb interaction (derived from a fundamental solution of the $S^3$ Laplace-Beltrami operator), a conformal $S^1\times S^3$ metric deformation is proposed, such that free motion on the deformed metric is equivalent to motion on the round metric in the presence of the interaction potential. We give explicit expressions for the generators of the conformal algebra in the representation induced by the metric deformation. By identifying the charge as the color degree of freedom in QCD, and the two charges system as a quark--anti-quark system, we argue that the associated conformal wave operator equation could provide a realistic quantum mechanical description of the simplest QCD system, the mesons. Finally, we discuss the possibility of employing the compactification radius, $R$, as another scale along ${\Lambda }_{QCD}$, by means of which, upon reparametrizing $Q^2{c}^2$ as $\left(Q^2{c}^2+{\hslash }^2{c}^2/R^2\right)$, a pertubative treatment of processes in the infrared could be approached.

arXiv commentMinor changes to match the published version

References in corpus (20)

• Gauge/string duality for QCD conformal operators
• A systematic study on the exact solution of the position dependent mass Schroedinger equation
• Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding
• Conformal Maxwell theory as a singleton field theory on AdS_5, IIB three-branes and duality
• Generalized Conformal and Superconformal Group Actions and Jordan Algebras
• Exceptional quantum geometry and particle physics
• Octonions, exceptional Jordan algebra and the role of the group F_4 in particle physics
• "Massive" Perturbative QCD, regular in the IR limit
• QCD with Chemical Potential in a Small Hyperspherical Box
• Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry
• The Principle of Relativity and Special Relativity Triple
• Conformally related massless fields in dS, AdS and Minkowski spaces
• Heavy quarkonia properties from a hard-wall confinement potential model with conformal symmetry perturbing effects
• Spectrum Generating Algebras for the free motion in $S^3$
• A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
• Modelling duality between bound and resonant meson spectra by means of free quantum motions on the de Sitter space time dS4
• Proton's Electromagnetic Form Factors from a Non-Power Confinement Potential
• Thermodynamic properties of the trigonometric Rosen-Morse potential and applications to a quantum gas of mesons
• Symmetry and degeneracy of the curved Coulomb potential on the S3 ball
• The conformally invariant vector field on $R\times S^3$

Cited by in corpus (3)

• Axiomatic de Sitter quantum Yang-Mills theory with color confinement and mass gap
• Potentials on the conformally compactified Minkowski spacetime and their application to quark deconfinement
• Saturation effect in confined quantum systems with energy-dependent potentials