On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry

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Abstract
A quantum procedure for the consistent treatment of general gauge theories with an arbitrary gauge-fixing in the presence of a soft breaking of BRST symmetry in the field-antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals, and therefore also that of the conventional $S$-matrix, for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve the consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of the functional renormalization group to the Yang--Mills and gravity theories. The Gribov--Zwanziger action and the refined Gribov--Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are perturbatively derived on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent both if the transformed BRST-breaking terms satisfy the soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge and without this requirement.

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