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We review the study of influence of the so-called soft BRST symmetry breakingwithin the Batalin-Vilkovisky (BV) formalism introduced in our papers [JHEP1110 (2011) 043, arXiv:1108.4820 [hep-th], MPLA 27 (2012) 1250067,arXiv:1201.4720 [hep-th]] on gauge dependence of the effective action andvacuum expectation values of gauge invariant operators. We derive the Wardidentities for generating functionals of Green's functions for a given theorywith soft BRST symmetry breaking term being added to the quantum action andinvestigate theirs gauge dependence. It is strongly argued that gauge theorieswith a soft breaking of BRST symmetry are inconsistent within the BV formalismbecause of the gauge-dependence of $S$-matrix. The application to theGribov-Zwanziger action (enlarging SU(N) Yang-Mills gauge theory by means ofnot gauge-invariant horizon function) for the one-parameter family of $R_\xi$gauges with use of the new form of the Hermitian augmented Faddeev-Popovoperator (being by Faddeev-Popov operator for transverse components ofYang--Mills fields) is considered.

Gauge dependence of vacuum expectation values of gauge invariant operators from soft breaking of BRST symmetry. Example of Gribov-Zwanziger action