SU(3) Polyakov linear-sigma model: Conductivity and viscous properties of QCD matter in thermal medium

In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-$\sigma$ model (PLSM) is analysed for chiral phase-transition, $\sigma_l$ and $\sigma_s$ and for deconfinement order-parameters, $\phi$ and $\phi^*$ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates ($\Delta_{l,s}$). All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modelling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric [$\sigma_{el}(T)$] and heat [$\kappa(T)$] conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, $\xi/s$ and $\eta/s$, respectively, and compared them with recent lattice QCD. Predictions for $(\xi /s)/(\sigma_{el}/T)$ and $(\eta/s)/(\sigma_{el}/ T)$ are introduced. We conclude that our results on various transport properties show some essential ingredients, that these properties likely come up with, in studying QCD matter in thermal and dense medium.