Spatial 't Hooft loop to cubic order in hot QCD

Spatial 't Hooft loops of strength k measure the qualitative change in the behaviour of electric colour flux in confined and deconfined phase of SU (N) gauge theory. They show an area law in the deconfined phase, known analytica lly to two loop order with a ``k-scaling'' law k(N-k). In this paper we comput e the O(g^3) correction to the tension. It is due to neutral gluon fields that get their mass through interaction with the wall. The simple k-scaling is lost in cubic order. The generic problem of non-convexity shows up in this order an d the cure is provided. The result for large N is explicitely given. We show tha t nonperturbative effects appear at O(g^5).Comment: 22 pages. Apart from a discussion on the renormalization effect of the Polyakov loop to cubic order only cosmetic changes with respect to the earlier hep-ph/021229

Two-loop perturbative corrections to the constrained effective potential in thermal QCD

In this paper, we compute the constrained QCD effective potential up to two-loop order with finite quark mass and chemical potential. We present the explicit calculations by using the double line notation and analytical expressions for massless quarks are obtained in terms of the Bernoulli polynomials or Polyakov loops. Our results explicitly show that the constrained QCD effective potential is independent on the gauge fixing parameter. In addition, as compared to the massless case, the constrained QCD effective potential with massive quarks develops a completely new term which is only absent when the background field vanishes. Furthermore, we discuss the relation between the one- and two-loop constrained effective potential. The surprisingly simple proportionality that exists in the pure gauge theories, however, is in general no longer true when fermions are taken into account. On the other hand, for high baryon density $\mu_B$ and low temperature $T$, in the massless limit, we do also find a similar proportionality between the one- and two-loop fermionic contributions in the constrained effective potential up to ${\cal O}(T/\mu_B)$.Comment: 36 pages, 5 figs, final version in JHE

Small shear viscosity in the semi quark gluon plasma

At nonzero temperature in QCD, about the deconfining phase transition there is a "semi" quark gluon plasma (semi-QGP), where the expectation value of the (renormalized) Polyakov loop is less than one. This can be modeled by a semiclassical expansion about a constant field for the vector potential, A_0, which is diagonal in color. We compute the shear viscosity in the semi-QGP by using the Boltzmann equation in the presence of this background field. To leading, logarithmic order in weak coupling, the dominant diagrams are given by the usual scattering processes of 2 -> 2 particles. For simplicity we also assume that both the number of colors and flavors are large. Near the critical temperature T_c, where the expectation value of the Polyakov loop is small, the overall density of colored fields decreases according to their color representation, with the density of quarks vanishes linearly with the loop, and that of gluons, quadratically. This decrease in the overall density dominates changes in the transport cross section. As a result, relative to that in the perturbative QGP, near T_c the shear viscosity in the semi-QGP is suppressed by two powers of the Polyakov loop. In a semiclassical expansion, the suppression of colored fields depends only upon which color representation they lie in, and not upon their mass. That light and heavy quarks are suppressed in a common manner may help to explain the behavior of charm quarks at RHIC.Comment: 45 pages, 8 figures, REVTeX; Abstract and Sec. III.A modified to clarify the physical discussion

Finite baryon density effects on gauge field dynamics

We discuss the effective action for QCD gauge fields at finite temperatures and densities, obtained after integrating out the hardest momentum scales from the system. We show that a non-vanishing baryon density induces a charge conjugation (C) odd operator to the gauge field action, proportional to the chemical potential. Even though it is parametrically smaller than the leading C even operator, it could have an important effect on C odd observables. The same operator appears to be produced by classical kinetic theory, allowing in principle for a non-perturbative study of such processes.Comment: 20 page

't Hooft and Wilson loop ratios in the QCD plasma

The spatial 't Hooft loop measuring the electric flux and the spatial Wilsonloop measuring the magnetic flux are analyzed in hot SU(N) gauge theory. Both display area laws. On one hand the tension of the 't Hooft loop is perturbatively calculable, in the same sense as the pressure. We show that the O(g^3) contribution is absent. The ratio of multi-charged 't Hooft loops have a remarkably simple dependence on the charge, true up to, but not including, O(g^4). This dependence follows also from a simple model of free screened colour charges. On the other hand the surface tension of the Wilsonloop is non-perturbative. But in a model of screened free monopoles at very high temperature the known area law follows. The density of these monopoles starts to contribute to O(g^6) to the pressure. The ratio of the multicharged Wilson loops is calculable and identical to that of the 't Hooft loops.Comment: 28 pages, 8 figure

Two loop renormalization of the magnetic coupling and non-perturbative sector in hot QCD

The goal of this paper is two-fold. The first aim is to present a detailed version of the computation of the two-loop renormalization of the magnetic coupling in hot QCD. The second is to compare with lattice simulations the string tension of a spatial Wilson loop using the result of our two-loop computationComment: 32 page