  The essence of the potential algebra concept [3] is that quantum mechanical
free motions of scalar particles on curved surfaces of given isometry algebras
can be mapped on 1D Schroedinger equations with particular potentials. As long
as the Laplace-Beltrami operator on a curved surface is proportional to one of
the Casimir invariants of the isometry algebra, free motion on the surface is
described by means of the eigenvalue problem of that very Casimir operator and
the excitation modes are classified according to the irreps of the algebra of
interest. In consequence, also the spectra of the equivalent Schroedinger
operators are classified according to the same irreps. We here use the
potential algebra concept as a guidance in the search for an interaction
describing conformal degeneracies. For this purpose we subject the so(4)
isometry algebra of the S^3 ball to a particular non-unitary similarity
transformation and obtain a deformed isometry copy to S^3 such that free motion
on the copy is equivalent to a cotangent perturbed motion on S^3, and to the 1D
Schroedinger operator with the trigonometric Rosen-Morse potential as well. The
latter presents itself especially well suited for quark-system studies insofar
as its Taylor series decomposition begins with a Cornell-type potential and in
accord with lattice QCD predictions. We fit the strength of the cotangent
potential to the spectra of the unflavored high-lying mesons and obtain a value
compatible with the light dilaton mass. We conclude that while the conformal
group symmetry of QCD following from AdS_5/CFT_4 may be broken by the dilaton
mass, it still may be preserved as a symmetry algebra of the potential, thus
explaining the observed conformal degeneracies in the unflavored hadron
spectra, both baryons and mesons.
