News from Lattice QCD on Heavy Quark Potentials and Spectral Functions of Heavy Quark States

We discuss recent lattice results on in-medium properties of hadrons and focus on thermal properties of heavy quark bound states. We will clarify the relation between heavy quark free energies and potentials used to analyze the melting of heavy quark bound states. Furthermore, we present calculations of meson spectral functions which indicate that the charmonium ground states, J/psi and eta_c, persist in the quark gluon plasma as well defined resonances with no significant change of their zero temperature masses at least up to T ~ 1.5 T_c. We also briefly comment on the current status of lattice calculations at non-vanishing baryon number density.Comment: Plenary talk at the 17th International Conference on Ultra Relativistic Nucleus-Nucleus Collisions (Quark Matter 2004), Oakland, California, 11-17 Jan 2004. Submitted to J.Phys.

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. 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 just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange