Holographic models in the T = 0 universality class of QCD in the limit of large number N c of colors and N f massless fermion flavors, but constant ratio x f = N f /N c , are analyzed at finite temperature. The models contain a 5-dimensional metric and two scalars, a dilaton sourcing TrF 2 and a tachyon dual toqq. The phase structure on the T, x f plane is computed and various 1st order, 2nd order transitions and crossovers with their chiral symmetry properties are identified. For each x f , the temperature dependence of p/T 4 and the condensate qq is computed. In the simplest case, we find that for x f up to the critical x c ∼ 4 there is a 1st order transition on which chiral symmetry is broken and the energy density jumps. In the conformal window x c < x f < 11/2, there is only a continuous crossover between two conformal phases. When approaching x c from below, x f → x c , temperature scales approach zero as specified by Miransky scaling.

A holographic model of QCD in the limit of large number of colors, N c , and massless fermion flavors, N f , but constant ratio x f = N f /N c is analyzed at finite temperature and chemical potential. The five dimensional gravity model contains three bulk fields: a scalar dilaton sourcing TrF 2 , a scalar tachyon dual toqq and a 4-vector dual to the baryon currentqγ µ q. The main result is the µ, T phase diagram of the holographic theory. A first order deconfining transition along T h (µ) and a chiral transition at T χ (µ) > T h (µ) are found. The chiral transition is of second order for all µ. The dependence of thermodynamical quantities including the speed of sound and susceptibilities on the chemical potential and temperature is computed. A new quantum critical regime is found at zero temperature and finite chemical potential. It is controlled by an AdS 2 × R 3 geometry and displays semi-local criticality.

We present a simple AdS/QCD model in which the formation of the chiral condensate is dynamically determined. The gauge dynamics is input through the running of the quark bilinear's anomalous dimension, γ. The condensate provides a dynamically generated infra-red wall in the computation of mesonic bound state masses and decay constants. As an example, we use the model, with perturbative computations of the running of γ, to study SU(3) gauge theory with a continuous number of quark flavours, N f . We follow the behaviour of the spectrum as we approach the conformal window through a walking gauge theory regime. We show such walking theories display a BKT phase transition, with Miransky scaling, as one approaches the edge of the conformal window at the critical value of N f . We show that these walking theories possess an enhanced quark condensate, a light Higgs like excitation and argue that the non-perturbative contribution to S falls to zero. We also study the deformation of the BKT transition when the quarks have a current mass which may be of use for understanding lattice simulations of walking theories.