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 $\zeta$ 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 $\zeta /s$ becomes rapidly small at high $T$, $\zeta /s<0.15$ at $1.65T_c$, and $\zeta /s<0.015$ at $3.2T_c$. However, $\zeta /s$ rises dramatically just above $T_c$, with $0.5<\zeta /s<2.0$ at $1.02T_c$.

• Received 26 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.162001