Shear viscosity to relaxation time ratio in SU(3) lattice gauge theory

TL;DR

This study calculates the shear viscosity to relaxation time ratio in SU(3) lattice gauge theory near the critical temperature, providing insights into gluon medium dynamics and hydrodynamic causality.

Contribution

It introduces a lattice-based method to evaluate the shear viscosity to relaxation time ratio using Euclidean correlators, near the critical temperature in SU(3) gauge theory.

Findings

The ratio is obtained for 1.3T_c to 4T_c with reasonable statistics.

The transverse wave speed in gluon media is approximately 0.5 for T > 1.5T_c.

The results are consistent with causality constraints in second order hydrodynamics.

Abstract

We evaluate the ratio of the shear viscosity to the relaxation time of the shear flux above but near the critical temperature $T_c$ 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 $1.3T_c \lesssim T \lesssim 4T_c$. We also found that the characteristic speed of the transverse plane wave in gluon media is almost constant, $v \simeq 0.5$, for $T \gtrsim 1.5T_c$, which is compatible with the causality in the second order dissipative hydrodynamics.