Transport coefficients and quasinormal modes in Einstein-dilaton holographic QCD

In this paper, we investigate the transport coefficients of a strongly coupled plasma in the context of holographic QCD models based on Einstein-dilaton gravity that are compatible with linear confinement at zero temperature. At finite temperature, the holographic model is characterized by an asymptotically anti–de Sitter black hole coupled to a scalar field, the dilaton, which is quadratic in the radial direction. The inclusion of the scalar field results in an explicit breaking of the conformal symmetry in the dual field theory. In such systems, the Hawking temperature of the black hole corresponds to the plasma temperature in the dual field theory. We confirm the existence of a minimum temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mi>min</a:mi></a:msub></a:math>, above which two distinct classes of black hole solutions emerge: one corresponding to large black holes and the other to small black holes. We calculate some thermodynamic quantities—such as entropy, specific heat, and speed of sound—and find results that are consistent with similar holographic models. We calculate the quasinormal modes of the tensor and vector sectors using the pseudospectral method. In the hydrodynamic regime, we derive the dispersion relation for the vector sector, from which we extract the shear viscosity and the ratio <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>η</c:mi><c:mo>/</c:mo><c:mi>s</c:mi><c:mo>=</c:mo><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>4</c:mn><c:mi>π</c:mi></c:math>. The bulk viscosity is calculated using the Kubo formula in the scalar sector. Finally, our results for the speed of sound are compared with the lattice QCD predictions, and our results for the bulk viscosity are compared with those reported by the JETSCAPE collaboration.