Renormalization of Polyakov loops in fundamental and higher representations

TL;DR

This paper compares two renormalization methods for Polyakov loops, finds their equivalence, and explores their behavior across different representations and temperatures, revealing Casimir scaling and screening effects in SU(3) gauge theory.

Contribution

It demonstrates the equivalence of two renormalization procedures and analyzes Polyakov loops in various representations, confirming Casimir scaling and screening phenomena.

Findings

Renormalization constants depend on the bare coupling.

Casimir scaling holds for higher representations.

Adjoint loops are small but non-zero below T_c, indicating screening.

Abstract

We compare two renormalization procedures, one based on the short distance behavior of heavy quark-antiquark free energies and the other by using bare Polyakov loops at different temporal extent of the lattice and find that both prescriptions are equivalent, resulting in renormalization constants that depend on the bare coupling. Furthermore these renormalization constants show Casimir scaling for higher representations of the Polyakov loops. The analysis of Polyakov loops in different representations of the color SU(3) group indicates that a simple perturbative inspired relation in terms of the quadratic Casimir operator is realized to a good approximation at temperatures $T \gsim T_c$ for renormalized as well as bare loops. In contrast to a vanishing Polyakov loop in representations with non-zero triality in the confined phase, the adjoint loops are small but non-zero even for temperatures below the critical one. The adjoint quark-antiquark pairs exhibit screening. This behavior can be related to the binding energy of gluelump states.