Baryons from quarks in curved space and deconfinement

Abstract

Detailed account is given of the fact that the Cornell potential predicted by Lattice QCD and its exactly solvable trigonometric extension recently reported by us can be viewed as the respective approximate and exact counterparts on a curved space to an 1/r flat space potential. The "curved" potential describes a confinement phenomenon because it is of infinite depth and has only bound states. It furthermore has the remarkable property of preserving both the SO(4) and SO(2,1) symmetries of the ordinary 1/r potential. We first make the case that this particular geometric version on confinement provides a remarkably adequate description of both nucleon and Delta spectra and the proton mean square charge radius as well, and suggests an intriguing venue toward quark deconfinement as shut-down of the curvature considered as temperature dependent. Next we observe that the SO(2,1) symmetry of the "curved" potential allows to place it within the context of AdS_5/CFT correspondence and to establish in this manner the algbraic link of the the latter to QCD potentiology.