Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge

The non-perturbative nilpotent exact BRST symmetry of the Gribov–Zwanziger action in the Landau gauge constructed in [1] is generalized to the case of Euclidean Yang–Mills theories quantized in the maximal Abelian gauge. The resulting diagonal gluon propagator is evaluating in dimensions D=4,3,2D=4,3,2. In D=4,3D=4,3 a decoupling type behavior is found in the infrared region, while in D=2D=2 a scaling type behavior emerges.