Non-perturbative dynamics of hot non-Abelian gauge fields

The dynamics of high temperature gauge fields, on scales relevant for non-perturbative phenomena such as electroweak baryogenesis, may be described by a remarkably simple effective theory. This theory, which takes the form of a local, stochastic, classical Yang-Mills theory, depends on a single parameter, the non-Abelian (or ``color'') conductivity. This effective theory has recently been shown to be valid to next-to-leading-log order (NLLO), provided one uses an improved NLLO value for the non-Abelian conductivity. Comparisons of numerical simulations using this NLLO effective theory and a more microscopic effective theory agree surprisingly well.Comment: 6 pages, based on talks at Quarks-2000 and SEWM-200

Z(3)-symmetric effective theory for SU(3) Yang-Mills theory at high temperature

A three-dimensional effective theory for high temperature SU(3) gauge theory, which maintains the Z(3) center symmetry of the full theory, is constructed. Such a Z(3) invariant effective theory should be applicable to a wider temperature range than the usual effective theory, known as EQCD, which fails to respect the center symmetry. This center-symmetric effective theory can reproduce domain wall and phase transition properties that are not accessible in EQCD. After identifying a convenient class of Z(3) invariant effective theories, we constrain the coefficients of the various terms in the Lagrangian using leading-order matching to EQCD at high temperature, plus matching of domain wall properties in the full theory. We sketch the expected structure of the phase diagram of the effective theory and briefly discuss the prospects of numerical simulations and the addition of quarks.Comment: 30 pages, 5 figures, v2 with minor correction

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.Comment: 70 pages, 19 figures; v4: fixed minus sign typo in last term of eqn. (3.47