Hints of (de)confinement in Yang-Mills-Chern-Simons theories in the maximal Abelian gauge

The study of Yang-Mills theories in three dimensions is an insightful playground to grasp important features for the four-dimensional case. Additionally, in three dimensions, the Chern-Simons term can be introduced with a mass parameter of topological nature. Quantizing such a theory in the continuum demands a gauge fixing which, in general, is plagued by Gribov copies. In this work, Yang-Mills-Chern-Simons theories are quantized in the maximal Abelian gauge and the existence of infinitesimal Gribov copies is taken into account. The elimination of copies modifies the (Abelian) gluon propagator leading to two different phases: one in which all poles are complex and thus interpreted as a confining phase and another where an excitation which can be part of the physical spectrum is present.