Shear viscosity of the gluon plasma in SU(3) YM theory is calculated nonperturbatively, within the stochastic vacuum model. The result for the ratio of the shear viscosity to the entropy density, proportional to the squared chromo-magnetic gluon condensate and the fifth power of the correlation length of the chromo-magnetic vacuum, falls off with the increase of temperature. At temperatures larger than the deconfinement critical temperature by a factor of 2, this fall-off is determined by the sixth power of the temperature-dependent strong-coupling constant and yields an asymptotic approach to the conjectured lower bound of 1/(4pi), achievable in {cal N}=4 SYM theory. As a by-product of the calculation, we find a particular form of the two-point correlation function of gluonic field strengths, which is the only one consistent with the Lorentzian shape of the shear-viscosity spectral function.
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