A holographic calculation of the electric conductivity of the strongly coupled quark-gluon plasma near the deconfinement transition

The frequency dependent conductivity $\sigma(\omega)$ of the strongly coupled Quark-Gluon Plasma (QGP) is estimated using a bottom up holographic model that can adequately describe recent lattice data for QCD thermodynamics at zero chemical potential. Different choices for the coupling between the bulk gauge field and the other bulk fields that define the background (the metric and a scalar field) are used in order to fit the lattice data for the electric charge susceptibility $\chi_2^Q/T^2$. The ratio $\sigma_{DC}/T$ is found to vary near the deconfinement transition in a way that is similar to recent lattice results. This model is used to compute the charge diffusion coefficient $D$ of the strongly coupled plasma. We find that the dimensionless combination $DT$ has the same type of temperature dependence displayed by $\sigma_{DC}/T$ and, thus, charge diffusion is suppressed at low temperatures. The frequency dependent conductivity $\sigma(\omega)$ reveals some nontrivial structure for values of the temperature near the phase transition. None of these structures appear in the associated Euclidean correlator, which we also compute. Our results suggest that the conformal invariance violation near the QCD deconfinement phase transition may be seen in the Euclidean correlator through a downward shift of its value at the minimum, which gives a rough estimate of the temperature dependence of the DC conductivity in the plasma.