Resumen:
We study relevance of conformal symmetry breaking through the dilaton mass on the high- lying spectra of the unflavored mesons. The conformal symmetry is supposed to leave a foot- print in those spectra in consequence of the gauge-gravity duality conjecture in combination with the opening of a conformal window in the infrared as recently observed experimental- ly through the property of the running coupling constant of QCD to approach a fixed point in the limit of a vanishing momentum transfer. The dilaton mass can affect the shape of the metric of the compactified Minkowski space-time, R1 × S3, one of the possible conformally invariant topologies embedded by AdS5 boundary, through a deformation of the S3 position space by a damping exponential factor.
Towards our purpose, we consider the mesons under investigation as four-dimensional rigid rotators with the quark performing free geodesic motion either on the S3 ball (unbroken con- formal symmetry), or, on the deformed metric (symmetry broken by the dilaton mass). We show that so(4) remains an isometry algebra of the deformed manifold though in a represen- tation unitarily-inequivalent to the one of the conformally invariant S3 surface. We further- more demonstrate that the Casimir invariant of the so(4) algebra describing the free motion on the deformed metric is equivalent to a perturbation of the free geodesic motion on S3 by a harmonic potential there and given by a cotangent function of the second polar angle parametrizing S3.
In solving the eigenvalue problem of the so(4) Casimir invariant on the deformed metric, we find same degeneracy patterns as on the undeformed. In this manner, a subtle mode of symmetry breaking has been identified in which the violation of the symmetry at the level of the representation function of the algebra can be opaqued by a conservation of the degeneracy patterns of the unbroken symmetry in the spectra.
