Polyakov loop correlator in perturbation theory

TL;DR

This paper investigates the perturbative structure of the Polyakov loop correlator, demonstrating its re-exponentiation into singlet and adjoint parts, and computes higher-order corrections in the short-distance regime.

Contribution

It provides a detailed perturbative analysis of the Polyakov loop correlator, including the order g^7 correction and the relation between different definitions of free energies.

Findings

Re-exponentiation into singlet and adjoint contributions is demonstrated.

Order g^7 correction to the correlator is calculated in the short-distance limit.

The relation between gauge invariant free energies and pNRQCD definitions is clarified.

Abstract

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order $g^7$ correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.