Conformal symmetry breaking and degeneracy of high-lying unflavored mesons Conference Paper uri icon

abstract

  • We show that though conformal symmetry can be broken by the dilaton, such can happen without breaking the conformal degeneracy patterns in the spectra. Our argumentation goes as follows: We departure from the gauge-gravity duality which predicts on the boundaries of the AdS5 geometry a conformal theory, associated with QCD at high temperatures, and consider S1 × S3 slicing. The inverse radius, R, of S3 relates to the temperature of the deconfinement phase transition and has to satisfy, hc/R ΛQCD. On S3, whose isometry group is SO(4), we then focus on the eigenvalue problem of the conformal Laplacian there, given by (k2%2b1), with standing for the Casimir invariant of the so(4) algebra. This eigenvalue problem describes the spectrum of a scalar particle, to be associated with a q system. Such a spectrum is characterized by a (K %2b l)2-fold degeneracy of its levels, with K [0, ). We then break the conformal S3 metric, ds2 dχ2 %2b sin 2 χ(dθ2 %2b sin2θd2) -in polar chi;,θ, and azimuthal coordinates- according to, ds ∼2 e-bχ((1 %2b b2/4)dχ2 %2b sin2 chi;(dθ2 %2b sin2θd 2)), and attribute the symmetry breaking scale bh2c 2/R2 to the dilaton. Next we show that the above metric deformation is equivalent to a breaking of the conformal curvature of S 3 by a term proportional to b cot χ, and that the perturbed conformal Laplacian is equivalent to (K2%2bck), with c κ a representation constant, and being again an so(4) Casimir invariant, but this time in a representation unitarily nonequivalent to the 4D rotational one. As long as the spectra before and after the symmetry breaking happen to be determined each by eigenvalues of a Casimir invariant of an so(4), no matter whether or not in a representation that generates the orthogonal group SO(4) as a subgroup of the conformal group SO(2,4), the degeneracy patterns remain unaltered though the conformal symmetry breaks at the level of the representation of the algebra. We fit the S3 radius and the h 2c2b/R2 scale to the high-lying excitations in the spectra of the unflavored mesons, and observe the correct tendency of the hc/R = 373 MeV value to notably exceed ΛQCD. The size of the symmetry breaking scale is calculated as MeV. © Published under licence by IOP Publishing Ltd.

publication date

  • 2012-01-01