Criticality from Einstein-Maxwell-dilaton holography at finite temperature and density

We investigate consistent charged black hole solutions to the Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a non-conformal plasma at finite temperature and density. For the dilaton we take a quadratic ansatz leading to linear confinement at zero temperature and density. We consider a grand canonical ensemble, where the chemical potential is fixed, and find a rich phase diagram involving the competition of small and large black holes. The phase diagram contains a critical line and a critical point similar to the van der Waals-Maxwell liquid-gas transition. As the critical point is approached, we show that the trace anomaly in the plasma phases vanishes signifying the restoration of conformal symmetry in the fluid. We find that the heat capacity and charge susceptibility diverge as $C_V \propto (T-T^c)^{-\alpha}$ and $\chi \propto (T-T^c)^{-\gamma}$ at the critical point with universal critical exponents $\alpha=\gamma=2/3$. Our results suggest a description of the thermodynamics near the critical point in terms of catastrophe theories. In the limit $\mu \to 0$ we compare our results with lattice results for $SU(N_c)$ Yang-Mills theories.