A holographic model for QCD in the Veneziano limit at finite temperature and density

Abstract

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 $\mathrm{Tr}{F}^2$, a scalar tachyon dual to $\bar{q}q$ and a 4-vector dual to the baryon current $\bar{q}{\gamma }^{\mu }q$. The main result is the $\mu ,T$ phase diagram of the holographic theory. A first order deconfining transition along $T_h(\mu )$ and a chiral transition at $T_{\chi }(\mu )>T_h(\mu )$ are found. The chiral transition is of second order for all $\mu$. 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${}_2\times R^3$ geometry and displays semi-local criticality.

Comments: 72 pages, 25 figures. In V2 a numerical error affecting a subset of numerical examples of v1 corrected, figures and text revised accordingly. In V3 the metadata abstract corrected to match the one in V2 manuscript