Field-Dependent BRST-antiBRST Lagrangian Transformations

Abstract

We continue our study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790[hep-th] and arXiv:1406.0179[hep-th]], with a doublet ${\lambda }_a$, $a=1,2$, of anticommuting Grassmann parameters and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179[hep-th]], which corresponds to a change of variables with functionally-dependent parameters ${\lambda }_a=U_a\Lambda$ induced by a finite Bosonic functional $\Lambda (\varphi ,\pi ,\lambda )$ and by the anticommuting generators $U_a$ of BRST-antiBRST transformations in the space of fields $\varphi$ and auxiliary variables ${\pi }^a,\lambda$. We obtain a Ward identity depending on the field-dependent parameters ${\lambda }_a$ and study the problem of gauge dependence, including the case of Yang--Mills theories. We examine a formulation with BRST-antiBRST symmetry breaking terms, additively introduced to the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge-independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST-antiBRST settings. These concepts are applied to the average effective action in Yang--Mills theories within the functional renormalization group approach.

20+7 pages, no figures, presentation improved, typos corrected, reference added, remarks on composite field approach added in Sec. 4 and App. B

References in corpus (18)

• Introduction to the functional RG and applications to gauge theories
• On the Functional Renormalization Group approach for Yang-Mills fields
• A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories
• Off-shell nilpotent finite BRST/anti-BRST transformations
• Is soft breaking of BRST symmetry consistent?
• A remark on the BRST symmetry in the Gribov-Zwanziger theory
• Field-dependent BRST transformations in Yang-Mills theory
• Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories
• Field dependent nilpotent symmetry for gauge theories
• Hamiltonian BRST-anti-BRST Theory
• Superfield formulation of the Lagrangian BRST quantization method
• Finite BRST-antiBRST Transformations in Lagrangian Formalism
• Soft breaking of BRST symmetry and gauge dependence
• Gribov ambiguities in the maximal Abelian gauge
• Effective Action of Composite Fields for General Gauge Theories in BLT-Covariant Formalism
• Finite BRST-antiBRST Transformations in Generalized Hamiltonian Formalism
• On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry
• A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

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• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon
• Comparative analysis of finite field-dependent BRST transformations
• Quantum gauge symmetry of reducible gauge theory
• Non-Abelian gauge theories with composite fields in the background field method