Abstract
Abstract 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 to $ \overline{q}q $ . 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 $ \left\langle {\overline{q}q} \right\rangle $ 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.
Highlights
QCD in the Veneziano limit [1], Nc → ∞, Nf → ∞, Nf Nc= xf fixed, λ = gY2 MNc fixed, (1.1)is expected to display a host of interesting and mostly non-perturbative phenomena, including: The “conformal window” with a nontrivial infrared (IR) fixed point, which extends from xf =11 2 to smaller values of xf
The system is in the thermal vacuum solution at low enough temperatures, jumps with a 1st order transition to the tachyon-hairy solution (the part of the blue line that is thick in figure 10) which still break chiral symmetry, and eventually smoothly transits to the red line at the point where the blue and red lines merge, via a chirally-restoring 2nd order transition
For large W0 it turns out that the solution with mq = 0 and nontrivial tachyon profile does not exist for very low xf, which explains the absence of chiral symmetry breaking
Summary
Is expected to display a host of interesting and mostly non-perturbative phenomena, including:. Near and below xc, there is the transition region to conventional QCD IR behavior In this region the theory is expected to be “walking”: This means that the theory appears to be approaching the IR fixed point as the coupling evolves very slowly for many e-foldings of energies. New phenomena are expected to appear at finite density driven by strong coupling and the presence of quarks These include color superconductivity [8, 9]. Discontinuities or rapid variations in pressure (or energy density) and quark condensate can be used to define phase boundaries associated with deconfinement and chiral symmetry restoration temperatures Td(xf ) and Tχ(xf ).
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