Polyakov loop and correlator of Polyakov loops at next-to-next-to-leading order

TL;DR

This paper computes the Polyakov loop and its correlator at high precision in the weak-coupling regime, providing detailed results up to next-to-next-to-leading order and employing effective field theory to analyze bound-state dynamics.

Contribution

It presents the first calculation of the Polyakov loop at order g^4 and the correlator at order g^6, incorporating an effective field theory approach for a systematic analysis.

Findings

Polyakov loop calculated at order g^4.

Correlator of two Polyakov loops computed at order g^6 for short distances.

Decomposition of correlator into gauge-invariant singlet and octet contributions.

Abstract

We study the Polyakov loop and the correlator of two Polyakov loops at finite temperature in the weak-coupling regime. We calculate the Polyakov loop at order g^4. The calculation of the correlator of two Polyakov loops is performed at distances shorter than the inverse of the temperature and for electric screening masses larger than the Coulomb potential. In this regime, it is accurate up to order g^6. We also evaluate the Polyakov-loop correlator in an effective field theory framework that takes advantage of the hierarchy of energy scales in the problem and makes explicit the bound-state dynamics. In the effective field theory framework, we show that the Polyakov-loop correlator is at leading order in the multipole expansion the sum of a colour-singlet and a colour-octet quark-antiquark correlator, which are gauge invariant, and compute the corresponding colour-singlet and colour-octet free energies.