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

Abstract

We perform a lattice Monte-Carlo calculation of the two-point functions of the energy-momentum tensor at finite temperature in the SU(3) gauge theory. Unprecedented precision is obtained thanks to a multi-level algorithm. The lattice operators are renormalized non-perturbatively and the classical discretization errors affecting the correlators are corrected for. A robust upper bound for the shear viscosity to entropy density ratio is derived, eta/s < 1.0, and our best estimate is eta/s = 0.134(33) at T=1.65Tc under the assumption of smoothness of the spectral function in the low-frequency region.

Figures (3)

• Figure 1: The correlators that contribute to $C(x_0)= {\frac{1}{4}}(C_{BB}+ C_{EE}+2C_{EB})$. Filled symbols correspond to $T=1.65T_c$, open symbols to $1.24T_c$. Error bars are smaller than the data symbols.
• Figure 2: The tree-level improved correlator $\overline C(x_0)$ normalized to the tree-level continuum infinite-volume prediction. The four points in each sequence are strongly correlated, but their covariance matrix is non-singular.
• Figure 3: The result for $\rho(\omega)$. The meaning of the error bands and the curves is described in the text. The area under them equals $\overline C(L_0/2)= 8.05(31)$ and 9.35(42) for $1.24T_c$ and $1.65T_c$ respectively.