Calculation of the shear viscosity in SU(3) gluodynamics

We perform a lattice Monte Carlo calculation of the two-point functions of the energy-momentum tensor at finite temperature in the SU(3) gauge theory. Unprecedented precision is obtained thanks to a multilevel algorithm. The lattice operators are renormalized nonperturbatively and the classical discretization errors affecting the correlators are corrected for. A conservative upper bound for the shear viscosity to entropy density ratio is derived, eta/s < 1.0, and our best estimate is eta/s=0.134(33) at T=1.65T(c) under the assumption of smoothness of the spectral function in the low-frequency region.