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

Abstract

We review the study of influence of the so-called soft BRST symmetry breaking within the Batalin-Vilkovisky (BV) formalism introduced in our papers [JHEP 1110 (2011) 043, arXiv:1108.4820 [hep-th], MPLA 27 (2012) 1250067, arXiv:1201.4720 [hep-th]] on gauge dependence of the effective action and vacuum expectation values of gauge invariant operators. We derive the Ward identities for generating functionals of Green's functions for a given theory with soft BRST symmetry breaking term being added to the quantum action and investigate theirs gauge dependence. It is strongly argued that gauge theories with a soft breaking of BRST symmetry are inconsistent within the BV formalism because of the gauge-dependence of $S$-matrix. The application to the Gribov-Zwanziger action (enlarging SU(N) Yang-Mills gauge theory by means of not gauge-invariant horizon function) for the one-parameter family of $R_{\xi }$ gauges with use of the new form of the Hermitian augmented Faddeev-Popov operator (being by Faddeev-Popov operator for transverse components of Yang--Mills fields) is considered.

15 pages, Contribution in Proceedings of the 17-th International Seminar QUARKS-2012, Yaroslavl, Russia, 4-10 June, 2012, misprints, expression (71) corrected, added formulae, discussion on Gribov region in covariant gauges; two indices in Eq.(72) corrected

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Cited by in corpus (5)

• Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories
• Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model
• On Composite fields approach to Gribov copies elimination in Yang-Mills theories
• Finite BRST-antiBRST Transformations for the Theories with Gauge Group
• On Consistent Lagrangian Quantization of Yang--Mills Theories without Gribov Copies