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

TL;DR

This paper calculates the shear viscosity of strongly interacting matter using a Nambu--Jona-Lasinio model with a comprehensive Kubo formalism, revealing a temperature and chemical potential dependence and a minimum near the AdS/CFT bound.

Contribution

It introduces a detailed calculation of shear viscosity in a NJL model using the full Dirac structure and mesonic fluctuations, avoiding on-shell approximations.

Findings

The ratio η/s decreases with temperature and chemical potential.

A minimum η/s slightly above 1/4π is found, interpolating between NJL and HTL results.

The method incorporates full spectral functions and mesonic fluctuations.

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.