Confinement, ghost sector and geometry in lattice gauge theories - Lachini, Nelson Pitanga (2019)
In this work we study the Gribov-Zwanziger scenario of confinement through lattice gauge theories. We start by reviewing continuum aspects of quantized Yang-Mills theories and the Faddeev-Popov method. After that, we present the gauge-copies problem and its potential resolution by restricting the path integral to the Gribov region, using the semiclassical computation as an illustration. Then we do a survey on lattice gauge theory and describe the main procedures and algorithms necessary to study the confinement problem numerically. At this point, we do a digress and review general features of confinement, from the well-known phenomenological models to the Green´s functions and center dominance approaches. Finally, we present simulations of the ghost-sector and the geometry of gaugespace for SU (2) theory. This includes a prescription for the discretization of BPST instanton backgrounds and the verification of their lattice topological charges. In that aspect, we show results supporting that instantons probably do not contribute to ghost enhancement. Also, using relatively small lattices, we compute the gluon and ghost propagators and the static quark-antiquark potential on vortex-only and vortex-removed ensembles through the so-called center projection and vortex removal procedures. We gather data that reproduce already published work in favor of the center dominance picture. Moreover, we are also able to present preliminary but novel results that numerically verify the localization of center vortices on the Gribov horizon and their probable consistency with massive-type solutions of the Dyson-Schwinger equations, besides a computation of the gluon propagator for pure SU (2) vortices.