We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that there is stronger attraction on distance scales on the order of the inverse Debye mass for quark pairs aligned along the direction of anisotropy than for transverse alignment.Comment: 8 pages, 2 figures, final version to appear in PLB, 1 reference added, numerical constant in Eq.(10) correcte

We consider quarkonium in a hot QCD plasma which, due to expansion and non-zero viscosity, exhibits a local anisotropy in momentum space. At short distances the heavy-quark potential is known at tree level from the hard-thermal loop resummed gluon propagator in anisotropic perturbative QCD. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coulomb field. At asymptotic separation the potential energy is non-zero and inversely proportional to the temperature. We obtain numerical solutions of the three-dimensional Schroedinger equation for this potential. We find that quarkonium binding is stronger at non-vanishing viscosity and expansion rate, and that the anisotropy leads to polarization of the P-wave states.Comment: 18 pages, 6 figures, final version, to appear in PR

We construct matrix models for the deconfining phase transition in SU (N ) gauge theories, without dynamical quarks, at a nonzero temperature T . We generalize models with zero [1] and one [2] free parameter to study a model with two free parameters: besides perturbative terms ∼ T 4 , we introduce terms ∼ T 2 and ∼ T 0 . The two N -dependent parameters are determined by fitting to data from numerical simulations on the lattice for the pressure, including the latent heat. Good agreement is found for the pressure in the semi-quark gluon plasma (QGP), which is the region from T c , the critical temperature, to about ∼ 4 T c . Above ∼ 1.2 T c , the pressure is a sum of a perturbative term, ∼ + T 4 , and a simple non-perturbative term, essentially just a constant times ∼ − T 2 c T 2 . For the pressure, the details of the matrix model only enter within a very narrow window, from T c to ∼ 1.2 T c , whose width does not change significantly with N .Without further adjustment, the model also agrees well with lattice data for the 't Hooft loop.This is notable, because in contrast to the pressure, the 't Hooft loop is sensitive to the details of the matrix model over the entire semi-QGP. For the (renormalized) Polyakov loop, though, our results disagree sharply with those from the lattice. Matrix models provide a natural and generic explanation for why the deconfining phase transition in SU (N ) gauge theories is of first order not just for three, but also for four or more colors. Lastly, we consider gauge theories where there is no strict order parameter for deconfinement, such as for a G(2) gauge group. To agree with lattice measurements, in the G(2) matrix model it is essential to add terms which generate complete eigenvalue repulsion in the confining phase. *