Monopole effects on Polyakov loop and its gauge independence in QCD

TL;DR

This paper demonstrates through lattice QCD simulations that monopole effects, represented by Dirac strings, are crucial for confinement and are gauge independent, with abelian Polyakov loops serving as order parameters for deconfinement.

Contribution

It provides evidence that monopole condensation is a gauge-independent mechanism for color confinement in QCD, based on abelian projection and lattice simulations.

Findings

Polyakov loops in abelian projection act as deconfinement order parameters.

Dirac strings cause the vanishing of Polyakov loops in the confinement phase.

Photon contributions remain finite in both phases.

Abstract

Monte-Carlo simulations of abelian projection in $T \neq 0$ pure lattice QCD show that 1)\ Polyakov loops written in terms of abelian link fields alone play a role of an order parameter of deconfinement transition 2)\ the abelian Polyakov loops are decomposed into contributions from Dirac strings of monopoles and from photons 3)\ vanishing of the abelian Polyakov loops in the confinement phase is due to the Dirac strings alone and the photons give a finite contribution in both phases. Moreover, these results appear to hold good in unitary gauges. This suggests that monopole condensation as the color confinement mechanism is gauge independent.