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Transport coefficients of two-flavor quark matter from the Kubo formalism

The transport coefficients of quark matter at non-zero chemical potential and temperature are computed within the two-flavor Nambu--Jona-Lasinio model. We apply the Kubo formalism to obtain the thermal ($κ$) and electrical ($σ$) conductivities as well as an update of the shear viscosity ($η$) by evaluating the corresponding equilibrium two-point correlation functions to leading order in the $1/N_c$ expansion. The Dirac structure of the self-energies and spectral functions is taken into account as these are evaluated from the meson-exchange Fock diagrams for on-mass-shell quarks. We find that the thermal and electrical conductivities are decreasing functions of temperature and density above the Mott temperature $T_{\rm M}$ of dissolution of mesons into quarks, the main contributions being generated by the temporal and vector components of the spectral functions. The coefficients show a universal dependence on the ratio $T/T_{\rm M}$ for different densities, i.e., the results differ by a chemical-potential dependent constant. We also show that the Wiedemann-Franz law for the ratio $σ/κ$ does not hold. The ratio $η/s $, where $s$ is the entropy density, is of order of unity (or larger) close to the Mott temperature and, as the temperature increases, approaches the AdS/CFT bound $1/4π$. It is also conjectured that the ratio $κT/c_V $, with $c_V$ being the specific heat, is bounded from below by $1/18$.