We study the role of QCD plasma instabilities in non-equilibrium quark-gluon plasmas. First, we argue that such instabilities must drastically modify the "bottom-up" thermalization scenario for heavy-ion collisions. Second, we discuss conditions for the existence of instabilities in a more general context than previously treated in the QCD literature. We also give a thorough qualitative review of the origin of instabilities. We discuss some mechanisms whereby the growth of plasma instabilities saturates. Finally, we solve explicitly for instabilities and their growth rates for two extreme cases of anisotropic non-equilibrium plasmas that can be treated relatively simply and analytically:is the distribution of particles in momentum space.1 Romatschke and Strickland [17] do obtain analytic results in a more general class of situations, but their results are unwieldy enough that they refrain from giving them explicitly in their paper. Also, another example of analysis of instabilities in ultra-relativistic plasmas, generalized to inclusion of a background magnetic field but restricted to wave vectors in certain symmetry directions, may be found in Ref. [18].

We study patterns of chiral symmetry breaking at zero temperature and its subsequent restoration at nonzero temperature within the SU(3) r ϫSU(3) l linear sigma model. Gap equations for the masses of the scalar and pseudoscalar mesons and the non-strange and strange quark condensates are systematically derived in the Hartree approximation via the Cornwall-Jackiw-Tomboulis formalism. In the chiral limit, the chiral symmetry restoring transition is found to be first order, as predicted by universality arguments. Taking the experimental values for the meson masses, however, the transition is crossover. The absence of the U(1) A anomaly is found to drive this transition closer to being first order. At large temperatures, the mixing angles between octet and singlet states approach ideal flavor mixing.

We discuss how to extract renormalized from bare Polyakov loops in SU (N ) lattice gauge theories at nonzero temperature. Single loops in an irreducible representation are multiplicatively renormalized, without mixing, through mass renormalization. The values of renormalized loops in the four lowest representations of SU (3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large N expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are powers of fundamental and anti-fundamental loops. The corrections to the large N relations at three colors are greatest for the sextet loop, ∼ 1/N , and are found to be ≤ 25%. The values of the renormalized triplet loop can be described by a matrix model, with an effective action dominated by the triplet loop: the deconfining phase transition for N = 3 is close to the Gross-Witten point at N = ∞.

Hydrodynamical modeling of heavy-ion collisions at RHIC suggests that the quark-gluon plasma (QGP) "thermalizes" in a remarkably short time scale, about 0.6 fm/c. We argue that this should be viewed as indicating fast isotropization, but not necessarily complete thermalization, of the nonequilibrium QGP. Non-Abelian plasma instabilities can drive local isotropization of an anisotropic QGP on a time scale which is faster than ordinary perturbative scattering processes. As a result, we argue that theoretical expectations based on weak-coupling analysis are not necessarily in conflict with hydrodynamic modeling of the early part of RHIC collisions, provided one recognizes the key role of non-Abelian plasma instabilities.

The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counterterm renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest.

QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what non-linear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge-fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities in the non-linear regime may have close parallels to similar processes in traditional plasma physics. We conjecture that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge theory becomes equivalent, respectively, to (i) traditional plasma physics, which is U(1) gauge theory, and (ii) plasma physics of U(1)×U(1) gauge theory.

We discuss homogeneous nucleation in a first-order chiral phase transition within an effective field theory approach to low-energy QCD. Exact decay rates and bubble profiles are obtained numerically and compared to analytic results obtained with the thin-wall approximation. The thin-wall approximation overestimates the nucleation rate for any degree of supercooling. The time scale for critical thermal fluctuations is calculated and compared to typical expansion times for high-energy hadronic or heavy-ion collisions. We find that significant supercooling is possible, and the relevant mechanism for phase conversion might be that of spinodal decomposition. Some potential experimental signatures of supercooling, such as an increase in the correlation length of the scalar condensate, are also discussed.

We study the deconfining phase transition in SU (N ) gauge theories at nonzero temperature using a matrix model of Polyakov loops. The most general effective action, including all terms up to two spatial derivatives, is presented. At large N , the action is dominated by the loop potential: following Aharony et al., we show how the Gross-Witten model represents an ultra-critical point in this potential. Although masses vanish at the Gross-Witten point, the transition is of first order, as the fundamental loop jumps only halfway to its perturbative value. Comparing numerical analysis of the N = 3 matrix model to lattice simulations, for three colors the deconfining transition appears to be near the Gross-Witten point. To see if this persists for N ≥ 4, we suggest measuring within a window ∼ 1/N 2 of the transition temperature.