Holographic models for QCD in the Veneziano limit

Abstract

Abstract We construct a class of bottom-up holographic models with physics comparable to the one expected from QCD in the Veneziano limit of large N f and N c with fixed $ x = \frac{{{N_f}}}{{{N_c}}} $ The models capture the holographic dynamics of the dilaton (dual to the YM coupling) and a tachyon (dual to the chiral condensate), and are parametrized by the real parameter x, which can take values within the range $ 0 \leqslant x < \frac{{{11}}}{{2}} $ . We analyze the saddle point solutions, and draw the phase diagram at zero temperature and density. The back-reaction of flavor on the glue is fully included. We find the conformal window for x ≥ x c, and the QCD-like phase with chiral symmetry breaking at x < x c, where the critical value x c lies close to four. We also find Miransky scaling as x → x c as well as Efimov-like saddle points. By calculating the holographic β-functions, we demonstrate the “walking” behavior of the coupling in the region near and below x c.