2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/181562We 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 \cite{Kaczmarek:2002mc} 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 $32^3\times 4,6,8$ lattices.4 pages, 4 figures, to appear in the proceedings of International Conference on Strong & Electroweak Matter 2006, Brookhaven National Laboratory, USA, May 10-13, 2006High Energy Physics - Latticetext