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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

We perform lattice calculations of the lightest J = 0, 2, 4, 6 glueball masses in the D=3+1 SU(3) gauge theory and extrapolate to the continuum limit. Assuming that these masses lie on linear Regge trajectories we find a leading glueball trajectory α(t) = 0.93(24) + 0.28(2)α ′ R t, where α ′ R ≃ 0.9 GeV −2 is the slope of the usual mesonic Regge trajectory. This glueball trajectory has an intercept and slope similar to that of the Pomeron trajectory. We contrast this with the situation in D=2+1 where the leading glueball Regge trajectory is found to have too small an intercept to be important for high-energy cross-sections. We interpret the observed states and trajectories in terms of open and closed string models of glueballs. We discuss the large-N limit and perform an SU(8) calculation that hints at new states based on closed strings in higher representations.

We calculate the light hadron spectrum in full QCD using two plus one flavor Asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size L ≈ 2.5 fm, and a lattice spacing of a ≈ 0.124 fm, for pion masses as light as mπ ≈ 300 MeV, and compared with the results by the MILC collaboration with Asqtad valence quarks at the same lattice spacing. Two-and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed-action heavy baryon chiral perturbation theory. Both the threeflavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order SU (3) fits are inconsistent with their phenomenological values. Nextto-next-to-leading order SU (2) continuum formulae provide a good fit to the data and yield and extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially lineaer in mπ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior.

Abstract. We discuss the calculation of the leading hadronic vacuum polarization in lattice QCD. Exploiting the excellent quality of the compiled experimental data for the e + e − → hadrons cross-section, we predict the outcome of large-volume lattice calculations at the physical pion mass, and design computational strategies for the lattice to have an impact on important phenomenological quantities such as the leading hadronic contribution to (g − 2)µ and the running of the electromagnetic coupling constant. First, the R(s) ratio can be calculated directly on the lattice in the threshold region, and we provide the formulae to do so with twisted boundary conditions. Second, the current correlator projected onto zero spatial momentum, in a Euclidean time interval where it can be calculated accurately, provides a potentially critical test of the experimental R(s) ratio in the region that is most relevant for (g − 2)µ. This observation can also be turned around: the vector correlator at intermediate distances can be used to determine the lattice spacing in fm, and we make a concrete proposal in this direction. Finally, we quantify the finite-size effects on the current correlator coming from low-energy two-pion states and provide a general parametrization of the vacuum polarization on the torus.

We consider the possibility of localizing gravity on a Nielsen-Olesen vortex in the context of the Abelian Higgs model. The vortex lives in a six-dimensional space-time with negative bulk cosmological constant. In this model we find a region of the parameter space leading, simultaneously, to warped compactification and to regular space-time geometry. A thin defect limit is studied. Regular solutions describing warped compactifications in the case of higher winding number are also presented.Comment: LaTeX, 39 pages, 21 figures, final version appeared in Nucl. Phys.