Polyakov loop in different representations of SU(3) at finite temperature

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 [O. Kaczmarek et al., Phys. Lett. B543 (2002) 41] 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.