Shear viscosity of a nonperturbative gluon plasma

Abstract

Shear viscosity is evaluated within a model of the gluon plasma, which is based entirely on the stochastic nonperturbative fields. We consider two types of excitations of such fields, which are characterized by the thermal correlation lengths ~ 1/(g^2 T) and ~ 1/(g^4 T), where "g" is the finite-temperature Yang-Mills coupling. Excitations of the first type correspond to the genuine nonperturbative stochastic Yang-Mills fields, while excitations of the second type mimic the known result for the shear viscosity of the perturbative Yang-Mills plasma. We show that the excitations of the first type produce only an O(g^{10})-correction to this result. Furthermore, a possible interference between excitations of these two types yields a somewhat larger, O(g^7), correction to the leading perturbative Yang-Mills result. Our analysis is based on the Fourier transformed Euclidean Kubo formula, which represents an integral equation for the shear spectral density. This equation is solved by seeking the spectral density in the form of the Lorentzian Ans\"atze, whose widths are defined by the two thermal correlation lengths and by their mean value, which corresponds to the said interference between the two types of excitations. Thus, within one and the same formalism, we reproduce the known result for the shear viscosity of the perturbative Yang-Mills plasma, and account for possible nonperturbative corrections to it.