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 AdS5 spacetime, topologically equivalent to the closed manifold S1× S3, 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 S3 Laplace-Beltrami operator), a conformal S1× S3 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 an- other scale along ΛQCD, by means of which, upon reparametrizing Q2c2 as (Q2c2+ħ2c2/R2), a perturbative treatment of processes in the infrared could be approached.
Highlights
By identifying the charge as the color degree of freedom in Quantum Chromodynamics (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
Taking the interaction potential as the analog of Coulomb interaction, a conformal S1 × S3 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
To the amount this equation is compatible with both the conformal symmetry of QCD in the infrared, signalled by the opening of the conformal window [11] on the one side, and the color-electric charge confinement on the other, we suggest it as a candidate for the quantum mechanical limit of QCD
Summary
Conformal compactification is a convenient way of ‘bringing infinity to a finite distance’. Each generatrix of the null cone N intersects the product S1 × Sd at two antipodal points, which must be identified in order to get a unique correspondence with ‘points at infinity’ for R1,d. The boundary at infinity corresponds to |y | → ∞, taken at a fixed point of S1 × S3, and can be asymptotically identified with the null-ray cone, L2 = 0, to the amount any finite value of L becomes negligible compared to the above mentioned limit [14]. Within the context of the AdS5/CF T4 gauge-gravity duality conjecture, on the AdS5 boundary (identified as above with the null-ray cone of R2,4 [14]) conformal field theories in their perturbative regimes can reside, some of which could appear dual to strongly coupled gravity in the bulk One theory of this kind is Quantum Electrodynamics (QED), which describes propagation of single charges. C1,3, of relevance to the perturbative ultraviolet regime of asymptotic freedom, the light front QCD has been developed [36], while in [18] M1,3 has been used in a perturbative approach to the QCD phase transition, in which the scale necessary for the introduction of temperature has been provided by the hyperradius of M1,3, treated as a small hyperspherical box with chemical potential
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
