Shear viscosity to relaxation time ratio in SU(3) lattice gauge theory
Abstract
We evaluate the ratio of the shear viscosity to the relaxation time of the shear flux above but near the critical temperature Tc in SU(3) gauge theory on the lattice. The ratio is related to Kubo's canonical correlation of the energy-momentum tensor in Euclidean space with the relaxation time approximation and an appropriate regularization. Using this relation, the ratio is evaluated by direct measurements of the Euclidean observables on the lattice. We obtained the ratio with reasonable statistics for the range of temperature 1.3Tc T 4Tc. We also found that the characteristic speed of the transverse plane wave in gluon media is almost constant, v 0.5, for T 1.5Tc, which is compatible with the causality in the second order dissipative hydrodynamics.
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