Deconfinement, Center Symmetry and the Ghost Propagator in Landau Gauge Pure SU(3) Yang-Mills Theory

TL;DR

This study investigates how the Landau gauge ghost propagator in pure SU(3) Yang-Mills theory varies with temperature, especially around the phase transition, suggesting its potential as an order parameter for confinement-deconfinement transition.

Contribution

It provides the first lattice QCD analysis of the ghost propagator's behavior across the deconfinement transition and explores its relation to center symmetry breaking.

Findings

Ghost propagator is enhanced at low momenta in the deconfined phase.

Decoupling of Polyakov loop sectors observed, similar to gluon propagator behavior.

Ghost propagator may serve as an order parameter for the phase transition.

Abstract

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, $T_c \sim 270$ MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, $\lesssim 1$ GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or $\pm 2\pi/3$ sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an "order parameter" for the confined-deconfined phase transition.