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In this work the shear viscosity of strongly interacting matter is calculatedwithin a two-flavor Nambu--Jona-Lasinio model as a function of temperature andchemical potential. The general Kubo formula is applied, incorporating the fullDirac structure of the thermal quark spectral function and avoiding commonlyused on-shell approximations. Mesonic fluctuations contributing via Fockdiagrams provide the dominant dissipative processes. The resulting ratio$\eta/s$ (shear viscosity over entropy density) decreases with temperature andchemical potential. Interpolating between our NJL results at low temperaturesand hard-thermal-loop results at high temperatures a minimum slightly above theAdS/CFT benchmark $\eta/s=1/4\pi$ is obtained.

Shear Viscosities from Kubo Formalism in a large-$N_{\rm c}$ Nambu--Jona-Lasinio Model