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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, η/s < 1.0, and our best estimate is η/s = 0.134(33) at T = 1.65Tc under the assumption of smoothness of the spectral function in the low-frequency region.PACS numbers: 12.38. Gc, 12.38.Mh, Introduction.-Models treating the system produced in heavy ion collisions at RHIC as an ideal fluid have had significant success in describing the observed flow phenomena [1,2]. Subsequently the leading corrections due to a finite shear viscosity were computed [3], in particular the flattening of the elliptic flow coefficient v 2 (p T ) above 1GeV. It is therefore important to compute the QCD shear and bulk viscosities from first principles to establish this description more firmly. Small transport coefficients are a signature of strong interactions, which lead to efficient transmission of momentum in the system. Strong interactions in turn require non-perturbative computational techniques. Several attempts have been made to compute these observables on the lattice in the SU(3) gauge theory [4,5]. The underlying basis of these calculations are the Kubo formulas, which relate each transport coefficient to a spectral function ρ(ω) at vanishing frequency. Even on current computers, these calculations are highly non-trivial, due to the fall-off of the relevant correlators in Euclidean time (as x −5 0 at short distances), implying a poor signal-to-noise ratio in a standard Monte-Carlo calculation. The second difficulty is to solve the ill-posed inverse problem for ρ(ω) given the Euclidean correlator at a finite set of points. Mathematically speaking, the uncertainty on a transport coefficient χ is infinite for any finite statistical accuracy, because adding ǫωδ(ω) to ρ(ω) merely corresponds to adding a constant to the Euclidean correlator of order ǫ, while rendering χ infinite. Therefore smoothness assumptions on ρ(ω) have to be made, which are reasonable far from the one-particle energy eigenstates, and can be proved in the hard-thermal-loop framework [6].

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

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