A calculation of the bulk viscosity in SU(3) gluodynamics

TL;DR

A lattice Monte Carlo calculation of the trace-anomaly two-point function at finite temperature in the SU(3) gauge theory is performed and the long distance properties of the correlator in the continuum limit are obtained and the bulk viscosity zeta is extracted via a Kubo formula.

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 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.

Figures (4)

• Figure 1: The correlator $C_\theta(x_0)$ on $L_0/a=8$ lattices.
• Figure 2: Continuum extrapolation of the first two moments $\langle\omega^0\rangle$ and $\langle\omega^2\rangle/(120T^2)$ of $\rho_\theta(\omega,T)$ for $T=1.24$ and $1.65T_c$. The $\langle\omega^0\rangle$ continuum limits are resp. $16.3(5)$ and $8.5(8)$.
• Figure 3: The result for $\rho_\theta(\omega)$ from $L_0/a=12$ lattices. The bulk viscosity is given by $\zeta/T^3=(\pi/18)\times {\rm intercept}$. The oscillating curve is the (rescaled) resolution function $\widehat{\delta}(0,\omega)$.
• Figure 4: The bulk viscosity in units of the entropy density, as a function of the conformality measure $\frac{\epsilon-3P}{\epsilon+P}$. The statistical errors are shown, as well as the bounds explained in the text. The solid line is the perturbative prediction Eq. \ref{['eq:LO']}, naively continued beyon $\alpha_s=0.3$ by the dashed line.