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In this paper, we take into account the Gribov copies present in 3DYang-MIlls-Higgs theory with a constant vector background whose presence breaksthe Lorentz symmetry. The constant vector background is introduced within thenon-Abelian aether term. Here, we show that this term arises as a one-loopcorrection. The influence of the aether coupling constant on the system istreated afterwards. As a result, we find that for some values of it the theorycan be driven from a nonperturbative regime to a perturbative one. In thispaper, we work with the Higgs field in the fundamental representation and inthe Landau gauge.

Regimes of $3D$ Yang--Mills theory in the presence of a constant vector background