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

Abstract

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

15 pages, 11 figures. Revision with minor corrections matches published version

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• Paramagnetic squeezing of a uniformly expanding quark-gluon plasma in and out of equilibrium
• Relativistic second-order dissipative hydrodynamics from Zubarev's non-equilibrium statistical operator
• Thermoelectric transport coefficients of quark matter