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We show that though conformal symmetry can be broken by the dilaton, such canhappen without breaking the conformal degeneracy patterns in the spectra. Wedeparture from R^1XS^3 slicing of AdS_5 noticing that the inverse radius, R, ofS^3 relates to the temperature of the deconfinement phase transition and has tosatisfy, \hbar c/R >> \Lambda_{QCD}. We then focus on the eigenvalue problem ofthe S^3 conformal Laplacian, given by 1/R^2 (K^2+1), with K^2 standing for theCasimir invariant of the so(4) algebra. Such a spectrum is characterized by a(K+1)^2 fold degeneracy of its levels, with K\in [0,\infty). We then break theconformal S^3 metric as, d\tilde{s}^2=e^{-b\chi} ((1+b^2/4) d\chi^2 +\sin^2\chi(d\theta ^2 +\sin^2\theta d\varphi ^2)), and attribute the symmetry breakingscale, b\hbar^2c^2/R^2, to the dilaton. We show that such a metric deformationis equivalent to a breaking of the conformal curvature of S^3 by a termproportional to b\cot \chi, and that the perturbed conformal Laplacian isequivalent to (\tilde{K}^2 +c_K), with c_K a representation constant, and\tilde{K}^2 being again an so(4) Casimir invariant, but this time in arepresentation unitarily inequivalent to the 4D rotational. In effect, thespectra before and after the symmetry breaking are determined each byeigenvalues of a Casimir invariant of an so(4) algebra, a reason for which thedegeneracies remain unaltered though the conformal group symmetry breaks at thelevel of the representation of its algebra. We fit the S^3 radius and the\hbar^2c^2b/R^2 scale to the high-lying excitations in the spectra of theunflavored mesons, and observe the correct tendency of the \hbar c /R=373 MeVvalue to notably exceed \Lambda_{QCD}. The size of the symmetry breaking scaleis calculated as \hbar c \sqrt{b}/R=673.7 MeV.

Conformal symmetry breaking and degeneracy of high-lying unflavored mesons