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

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 ${\rm Tr}F^2$, a scalar tachyon dual to $\bar qq$ 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.