The Polyakov loop at next-to-next-to leading order

TL;DR

This paper computes the next-to-next-to-leading order correction to the Polyakov loop expectation value in SU(3) gauge theory, revealing its proportionality to the quadratic Casimir and comparing with lattice data.

Contribution

It provides the first calculation of the $g^5$ order correction to the Polyakov loop and demonstrates its proportionality to the quadratic Casimir operator.

Findings

Correction of order $g^5$ computed.

Polyakov loop proportional to quadratic Casimir.

Comparison with recent lattice results included.

Abstract

We calculate the next-to-next-to-leading correction to the expectation value of the Polyakov loop or equivalently to the free energy of a static charge. This correction is of order $g^5$. We show that up to this order the free energy of the static charge is proportional to the quadratic Casimir operator of the corresponding representation. We also compare our perturbative result with the most recent lattice results in SU(3) gauge theory.