We present a renormalization procedure for Polyakov loops which explicitly implements the fact that the renormalization constant depends only on the ultraviolet cutoff. Using this we study the renormalized Polyakov loops in all representations upto the 27 of the gauge group SU(3). We find good evidence for Casimir scaling of the Polyakov loops and for approximate large-N factorization. By studying many loops together, we are able to show that there is a matrix model with a single coupling which can describe the high temperature phase of QCD, although it is hard to construct explicitly. We present the first results for the non-vanishing renormalized octet loop in the thermodynamic limit below the SU(3) phase transition, and estimate the associated string breaking distance and the gluelump binding energy. By studying the connection of the direct renormalization procedure with a generalization of an earlier suggestion which goes by the name of the QQ renormalization procedure, we find that they are functionally equivalent.

We analyze the screening of static diquark sources in 2-flavor QCD and compare results with the screening of static quark-antiquark pairs. We show that a two quark system in a fixed color representation is screened at short distances like a single quark source in the same color representation whereas at large distances the two quarks are screened independently. At high temperatures we observe that the relative strength of the interaction in diquark and quark-antiquark systems, respectively, obeys Casimir scaling. We use this result to examine the possible existence of heavy quark-quark bound states in the high temperature phase of QCD. We find support for the existence of bb states up to about 2Tc while cc states are unlikely to be formed above Tc.

We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3 þ 1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions of the trace of the energy-momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport coefficients, in particular, the bulk viscosity, in the vicinity of a second order phase transition point.

We investigate the Polyakov loop in different representations of SU(3) in pure gauge at finite T . We discuss Casimir scaling for the Polyakov loop in the deconfined phase and test and generalize the renormalization procedure for the Polyakov loop from [ 1] to arbitrary representations. In the confined phase we extract the renormalized adjoint Polyakov loop, which is finite in the thermodynamic limit. For our numerical calculations we used the tree-level improved Symanzik action on 32 3 × 4, 6, 8 lattices. The Polyakov loop in different representationsWe define the thermal Wilson line in representation rwhere U t are the temporal gauge links in representation r. The Polyakov loop in representation r is thenwhere Tr 1 = 1. We obtain L r (x) from L 3 (x) by the aid of the character property of the direct product representation χ p⊗q (g) = χ p (g)χ q (g) (see table I in [ 2]). The expectation value of the Polyakov loop is then obtained bywhere V 3 is the spatial volume of the lattice. We have calculated the expectation values of the Polyakov loop in higher representations up to r = 15a in pure gauge theory. Renormalization and Casimir scalingRealizing that the renormalization constants only depend on the bare coupling [ 3], Z r (g 2 ), the renormalized Polyakov loop can be obtained from the bare loops at different N τ . As any renormalization procedure is fixed up to a multiplicative constant , i. e. L c r =

We study the free energy of static three quark systems in singlet, octet, decuplet and average color channels in the quenched approximation and in 2-flavor QCD at finite temperature. We show that in the high temperature phase singlet and decuplet free energies of three quark systems are well described by the sum of the free energies of three diquark systems plus self energy contributions of the three quarks. In the confining low temperature phase we find evidence for a Y-shaped flux tube in SU(3) pure gauge theory, which is less evident in 2-flavor QCD due to the onset of string breaking. We also compare the short distance behavior of octet and decuplet free energies to the free energies of single static quarks in the corresponding color representations.Comment: 11 pages, 17 figure