Calculation of the Bulk Viscosity in SU(3) Gluodynamics

Abstract

We perform a lattice Monte Carlo calculation of the trace-anomaly two-point function at finite temperature in the SU(3) gauge theory. We obtain the long distance properties of the correlator in the continuum limit and extract the bulk viscosity $\ensuremath{\zeta}$ via a Kubo formula. Unlike the tensor correlator relevant to the shear viscosity, the scalar correlator depends strongly on temperature. If $s$ is the entropy density, we find that $\ensuremath{\zeta}/s$ becomes rapidly small at high $T$, $\ensuremath{\zeta}/s<0.15$ at $1.65{T}_{c}$, and $\ensuremath{\zeta}/s<0.015$ at $3.2{T}_{c}$. However, $\ensuremath{\zeta}/s$ rises dramatically just above ${T}_{c}$, with $0.5<\ensuremath{\zeta}/s<2.0$ at $1.02{T}_{c}$.