Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

•We implement the Gribov quantization to the Topologically massive Yang–Mills theory.•We find a modified propagator at strong coupling by the Gribov horizon.•The gauge propagator depends on the topological mass and the coupling constant.•By studying the gauge propagator we describe the confined–deconfined regimes.

The two-point gauge correlation function in Yang–Mills–Chern–Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory.