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

TL;DR

This paper studies the behavior of the Polyakov loop across different representations of SU(3) gauge theory at finite temperature, focusing on Casimir scaling, renormalization, and numerical results in pure gauge theory.

Contribution

It generalizes the renormalization procedure for Polyakov loops to arbitrary representations and provides numerical results for the adjoint Polyakov loop in the confined phase.

Findings

Casimir scaling observed in the deconfined phase

Renormalized adjoint Polyakov loop is finite in the thermodynamic limit

Numerical results obtained using Symanzik improved action on various lattice sizes

Abstract

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 \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.