The Polyakov Loop and its Relation to Static Quark Potentials and Free Energies

TL;DR

This paper clarifies the correct interpretation of Polyakov loop correlators, demonstrating that all channels are dominated by singlet states and providing a corrected definition of the singlet free energy, supported by lattice simulations.

Contribution

It corrects misconceptions about Polyakov loop channels, showing they all originate from singlet states and offers a refined definition of the singlet free energy.

Findings

All channels receive contributions solely from singlet states.

The corrected singlet free energy is consistent with simulation results.

Simulations of 3d SU(2) gauge theory support the analytical findings.

Abstract

It appears well accepted in the literature that the correlator of Polyakov loops in a finite temperature system decays with the "average" free energy of the static quark-antiquark system, and can be decomposed into singlet and adjoint (or octet for QCD) contributions. By fixing a gauge respecting the transfer matrix, attempts have been made to extract those contributions separately. In this paper we point out that the "average" and "adjoint" channels of Polyakov loop correlators are misconceptions. We show analytically that all channels receive contributions from singlet states only, and give a corrected definition of the singlet free energy. We verify this finding by simulations of the 3d SU(2) pure gauge theory in the zero temperature limit, which allows to cleanly extract the ground state exponents and the non-trivial matrix elements. The latter account for the difference between the channels observed in previous simulations.