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A holographic model of QCD in the limit of large number of colors, $N_c$, andmassless fermion flavors, $N_f$, but constant ratio $x_f=N_f/N_c$ is analyzedat finite temperature and chemical potential. The five dimensional gravitymodel contains three bulk fields: a scalar dilaton sourcing ${\rm Tr}F^2$, ascalar 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 theholographic theory. A first order deconfining transition along $T_h(\mu)$ and achiral transition at $T_\chi(\mu)>T_h(\mu)$ are found. The chiral transition isof second order for all $\mu$. The dependence of thermodynamical quantitiesincluding the speed of sound and susceptibilities on the chemical potential andtemperature is computed. A new quantum critical regime is found at zerotemperature and finite chemical potential. It is controlled by an AdS$_2\timesR^3$ geometry and displays semi-local criticality.

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