Temperature dependence of shear viscosity of $SU(3)$--gluodynamics within lattice simulation

Abstract

In this paper we study the shear viscosity temperature dependence of $SU(3)$--gluodynamics within lattice simulation. To do so, we measure the correlation functions of energy-momentum tensor in the range of temperatures $T/T_c\in [0.9, 1.5]$. To extract the values of shear viscosity we used two approaches. The first one is to fit the lattice data with some physically motivated ansatz for the spectral function with unknown parameters and then determine shear viscosity. The second approach is to apply the Backus-Gilbert method which allows to extract shear viscosity from the lattice data nonparametrically. The results obtained within both approaches agree with each other. Our results allow us to conclude that within the temperature range $T/T_c \in [0.9, 1.5]$ SU(3)--gluodynamics reveals the properties of a strongly interacting system, which cannot be described perturbatively, and has the ratio $\eta/s$ close to the value ${1}/{4\pi}$ in $N = 4$ Supersymmetric Yang-Mills theory.