On the Faddeev-Popov operator eigenspectrum in topological background fields

Abstract

During the last years significant progress has been made in the understanding of the confinement of quarks and gluons. However, this progress has been made in two directions, which are at first sight very different. On the one hand, topological configurations seem to play an important role in the formation of the static quarkanti-quark potential. On the other hand, when studying Green's functions, the Faddeev-Popov operator seems to be of importance, especially its spectrum near zero. To investigate whether a connection between both aspects exist, the eigenspectrum of the Faddeev-Popov operator in an instanton and a center-vortex background field are determined analytically in the continuum. It is found that both configurations give rise to additional zero-modes. This agrees with corresponding studies of vortices in lattice gauge theory. In the vortex case also one necessary condition for the confinement of color is fulfilled. Some possible consequences of the results will be discussed, and also a few remarks on monopoles will be given.

Ghost and gluon propagators of quenched lattice QCD: NSPT vs. Monte Carlo results

“…On the other hand, the identification of the nonperturbative enhancement of the gluon and ghost propagators in the intermediate momentum range, over the behavior predicted by plain perturbation theory is of particular interest, too. It has been put into relation to effects of instantons [16] and shown to depend on the presence of confining degrees of freedom like vortices [17,18,19].…”