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

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.