It is shown that the nucleon and Delta(1232) resonances reported so far form parts of irreducible representations of the conformal group. This phenomenon finds its stringent explication within the context of AdS$5$/CFT$_4$ correspondence. According to the latter, it is believed that each state of a CFT, such like (approximately) QCD, on the conformal boundary, {\bf R}$^{1}\times S^{3} $, of $AdS{4+1}$ can be related to a state in the supergravity approximation to string theory on $AdS_{4+1}\times S^3$ meaning that spectra in both theories should be same. This observation justifies modeling spectra on {\bf R}$\times S^3$. We here present our recently developed quark model on $S^3$ with the angular $\cot \chi $ potential that depends on the second polar angle ($\chi$) alone, and which has the conformal group as a dynamical symmetry. We reveal adequacy of the $\cot $-spectrum for the description of the observed light $N$ and $\Delta$ baryon spectra. For various parameterizations of the $S^3$ angular variable $\chi$ in terms of a properly defined three dimensional radius vector, $r$, the $\cot \chi (r)$ potential is shown to contain as leading terms of its Taylor series decomposition the Coulombic+linear potential which is one of the possible AdS/CFT Wilson loop potentials, on the one side, and which coincides with the Cornell potential confirmed by Lattice QCD, on the other. The extra terms in the $\cot \chi (r)$ expansions acquire meaning of non-perturbative corrections. We furthermore draw attention to the fact that the cotangent potential on $S^3$ can be equivalently transformed to the Wilson loop potential $\sech^2$ on the AdS$_{2+1}$ hyperboloid. Such a potential has been recently obtained for the case of open strings ending on branes in a space that can be viewed as a portion of a flat Minkowski space, expressed in coordinates adapted to an observer at constant acceleration (so called Rindler space).

We employ the developed formalism in the design of a dressing function for the gluon propagator from Fourier transforming the potential under investigation and find it finite in the infrared while approaching zero in the ultraviolet.