Paper detail

Exploring new horizons of the Gribov problem in Yang-Mills theories

The understanding of the non-perturbative regime of YM theories remains a challenging open problem in theoretical physics. Notably, a satisfactory description of the confinement of gluons is not at our disposal so far. In this thesis, the RGZ framework, designed to provide a proper quantization of YM theories by taking into account the existence of the so-called Gribov copies is explored. Successfully introduced in the Landau gauge, the RGZ set up does not extend easily to different gauges. The main reason is that a clear formulation of the analogue of the Gribov horizon in the Landau gauge is obstructed by technical difficulties when more sophisticated gauges are chosen. Moreover, the RGZ action breaks BRST symmetry explicitly, making the task of extracting gauge invariant results even more difficult. The main goal of the present thesis is precisely to provide a consistent framework to extend the RGZ action to gauges that are connected to Landau gauge via a gauge parameter. Our main result is the reformulation of the theory in the Landau gauge with appropriate variables such that a non-perturbative BRST symmetry is constructed. This symmetry corresponds to a deformation of the standard BRST symmetry by taking into account non-perturbative effects. This opens a toolbox which allow us to explore what would be the Gribov horizon in different gauges as linear covariant and Curci-Ferrari gauges. Consistency with gauge independence of physical quantities as well as the computation of the gluon propagator in these gauges is provided. Remarkably, when lattice or functional methods results are available, we verify very good agreement with our analytical proposal giving support that it could provide some insights about the non-perturbative regime of YM theories. A positivity violating gluon propagator in the infrared seems to be a general feature of the formalism.