Effective holographic models for QCD: Thermodynamics and viscosity coefficients.

A finite temperature extension of the effective holographic models for QCD (EHQCD), proposed in Ref.~\cite{Ballon-Bayona:2017sxa}, is investigated in the present work. EHQCD models are characterized by two parameters, the conformal dimension of the relevant operator that deforms the CFT and the associated coupling. We find that black hole solutions appear at temperatures higher than some temperature $T_{min}$ and can be categorized in two classes: large and small black holes. The large black hole is always thermodynamically stable and it is therefore interpreted as the gravity dual of the non-conformal plasma. The small black hole, on the other hand, is always thermodynamically unstable. We show that thermodynamic quantities such as the entropy density $s$, specific heat $C_V$, and speed of sound $c_s$ are sensitive to the model parameters. We investigate perturbations of the black hole solutions and calculate the viscosity coefficients of the non-conformal plasma. For the shear viscosity, we confirm that the ratio $\eta/s$ is given by the universal result $1/4\pi$. For the bulk viscosity, the ratio $\zeta/s$ varies with the temperature, displaying a rapid growth close to $T_{min}$, and is sensitive to the model parameters. We compare our results for the thermodynamic quantities against lattice $SU(N_C)$ results and find that they are compatible as long as the coupling is fixed appropriately as a function of the conformal dimension. We also compare our results for the viscosity coefficients against the JETSCAPE results, obtained from the analysis of heavy ion collision experimental data.