We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled N = 4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Müller-Israel-Stewart theory, often used in numerical simulations, does not contain all allowed second-order terms and, frequently, terms required by conformal invariance.

Relativistic viscous hydrodynamic fits to RHIC data on the centrality dependence of multiplicity, transverse and elliptic flow for √ s = 200 GeV Au+Au collisions are presented. For standard (Glauber-type) initial conditions, while data on the integrated elliptic flow coefficient v2 is consistent with a ratio of viscosity over entropy density up to η/s ≃ 0.16, data on minimum bias v2 seems to favor a much smaller viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some caveats on this result are discussed.The success of ideal hydrodynamics for the description of heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) has led to the idea of a quark-gluon plasma behaving as a "perfect liquid", with a very small ratio of viscosity over entropy density [1,2,3,4]. An answer to the question "How perfect is the fluid observed at RHIC?" can, however, not be found using ideal hydrodynamics, but must involve a controlled quantitative understanding of non-idealities, e.g. viscous effects. If hydrodynamics can be applied to RHIC physics, then relativistic viscous hydrodynamics should be able to provide such an understanding. In particular, if one has control over the initial conditions, it should be possible to determine the size of various hydrodynamic transport coefficients, such as the shear viscosity, by a best fit of viscous hydrodynamics (VH) to experimental data. In this Letter, we aim to take a step in this direction.For RHIC physics, since particle number in the quarkgluon plasma is ill-defined, the relevant dimensionless parameter for VH is the ratio shear viscosity η over entropy density s. Based on the correspondence between Anti-deSitter (AdS) space and conformal field theory (CFT), it has been conjectured [5] that all relativistic quantum field theories at finite temperature and zero chemical potential have η/s ≥ 1 4π . To date, no physical system violating this bound has been found.Neglecting effects from bulk viscosity and heat conductivity, the energy momentum tensor for relativistic hydrodynamics in the presence of shear viscosity isIn Eq.(1), ǫ and p denote the energy density and pressure, respectively, and u µ is the fluid 4-velocity which obeys g µν u µ u ν = 1 when contracted with the metric g µν . The shear tensor Π µν is symmetric, traceless (Π µ µ = 0), and orthogonal to the fluid velocity, u µ Π µν = 0. Conservation of the energy momentum tensor and equation of state provide five equations for the evolution of the 10 independent components of ǫ, p, u µ , Π µν . The remaining five equations for the evolution of Π µν are not unambiguously agreed on at present [6,7,8,9,10]. The results in this work will be based on using the set of equationswhere d α is the covariant derivative, used to construct the time-like and space-like derivatives∆ µν ∇ α u α and the vorticity ω µν = ∇ ν u µ −∇ µ u ν . Both p and temperature T are related to ǫ via the QCD equation of state, for which we take the semi-realistic result from Ref. [11]. If the relaxation time τ Π is not too small, Eq...

We derive a static potential for a heavy quark-antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Green's function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye-screened potential could be used in models that attempt to describe the "melting" of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal effects generate a finite width for the quarkonium peak in the dilepton production rate. For quarkonium with a very heavy constituent mass M , the width can be ignored for T < ∼ g 2 M/12π, where g 2 is the strong gauge coupling; for a physical case like bottomonium, it could become important at temperatures as low as 250 MeV. Finally, we point out that the physics related to the finite width originates from the Landau-damping of low-frequency gauge fields, and could be studied non-perturbatively by making use of the classical approximation.

We analyze the collective modes of high-temperature QCD in the case when there is an anisotropy in the momentum-space distribution function for the gluons. We perform a tensor decomposition of the gluon self-energy and solve the dispersion relations for both stable and unstable modes. Results are presented for a class of anisotropic distribution functions which can be obtained by stretching or squeezing an isotropic distribution function along one direction in momentum space. We find that there are three stable modes and either one or two unstable modes depending on whether the distribution function is stretched or squeezed. The presence of unstable modes which have exponential growth can lead to a more rapid thermalization and isotropization of the soft modes in a quark gluon plasma and therefore may play an important role in the dynamical evolution of a quark-gluon plasma.

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Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of applicability, and can be applied to both weakly and strongly coupled systems. In its modern formulation, relativistic viscous hydrodynamics can directly be solved numerically. This has been useful for the problem of ultrarelativistic heavy-ion collisions, and I will review the setup and results of a hydrodynamic description of experimental data for this case. Contents

We perform an Oð 2 s Þ perturbative calculation of the equation of state of cold but dense QCD matter with two massless and one massive quark flavor, finding that perturbation theory converges reasonably well for quark chemical potentials above 1 GeV. Using a running coupling constant and strange quark mass, and allowing for further nonperturbative effects, our results point to a narrow range where absolutely stable strange quark matter may exist. Absent stable strange quark matter, our findings suggest that quark matter in (slowly rotating) compact star cores becomes confined to hadrons only slightly above the density of atomic nuclei. Finally, we show that equations of state including quark matter lead to hybrid star masses up to M $ 2M , in agreement with current observations. For strange stars, we find maximal masses of M $ 2:75M and conclude that confirmed observations of compact stars with M > 2M would strongly favor the existence of stable strange quark matter.

We present first results for 3+1-D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time τ as exp(Γ g 2 µτ ), where g 2 µ is a scale arising from the saturation of gluons in the nuclear wavefunction. The scale for the growth rate Γ is set by a plasmon mass, defined as ω pl = κ0 g 2 µ τ , generated dynamically in the collision. We compare the numerical ratio Γ/κ0 to the corresponding value predicted by the Hard Thermal Loop formalism for anisotropic plasmas.