The discontinuities of conformal transitions and mass spectra of V-QCD

Zero temperature spectra of mesons and glueballs are analyzed in a class of holographic bottom-up models for QCD in the Veneziano limit, N_c -> infinity, N_f -> infinity, with x = N_f/N_c fixed (V-QCD). The backreaction of flavor on color is fully included. It is found that spectra are discrete and gapped (modulo the pions) in the QCD regime, for x below the critical value x_c where the conformal transition takes place. The masses uniformly converge to zero in the walking region x -> x_c^- due to Miransky scaling. All the ratios of masses asymptote to non-zero constants as x -> x_c^- and therefore there is no "dilaton" in the spectrum. The S-parameter is computed and found to be of O(1) in units of N_f N_c in the walking regime, while it is always an increasing function of x. This indicates the presence of a subtle discontinuity of correlation functions across the conformal transition at x = x_c.