Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories

Abstract

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet ${\lambda }_a$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with $s_a$-potential parameters ${\lambda }_a=s_a\Lambda$ induced by a finite even-valued functional $\Lambda$ and by the anticommuting generators $s_a$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary $R_{\xi }$-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional $h$, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST\ transformations to the case of general gauge theories and present an ansatz for such transformations.

31 pages, no figures, misprint in the Eq. (5.1) corrected

References in corpus (10)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Radiation Pressure Acceleration by Ultraintense Laser Pulses
• Off-shell nilpotent finite BRST/anti-BRST transformations
• A remark on the BRST symmetry in the Gribov-Zwanziger theory
• Finite BRST-antiBRST Transformations in Lagrangian Formalism
• A systematic study of finite BRST-BV transformations in field-antifield formalism
• Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge
• Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model
• Gribov-Zwanziger action in SU(2) Maximally Abelian Gauge with U(1)${}_3$ Landau Gauge
• On Composite fields approach to Gribov copies elimination in Yang-Mills theories

Cited by in corpus (30)

• Finite field-dependent BRST symmetry for ABJM theory in $\mathcal{N}=1$ superspace
• Finite BRST-antiBRST Transformations in Lagrangian Formalism
• Influence of Gribov ambiguities in a class of nonlinear covariant gauges
• IR finite graviton propagators in de Sitter spacetime
• Comments on interactions in the SUSY models
• Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model
• Maximal Abelian gauge and a generalized BRST transformation
• Field-Dependent BRST-antiBRST Lagrangian Transformations
• Accessing the topological susceptibility via the Gribov horizon
• Non-perturbative to perturbative QCD via the FFBRST
• BRST Quantization of Unimodular Gravity
• Finite BRST-antiBRST Transformations in Generalized Hamiltonian Formalism
• On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry
• Refined Gribov-Zwanziger theory coupled to scalar fields in the Landau gauge
• Finite Field-dependent Symmetry in Thirring Model
• Exploring new horizons of the Gribov problem in Yang-Mills theories
• Super-group field cosmology in Batalin-Vilkovisky formulation
• Finite BRST Mapping in Higher Derivative Models
• Hints of (de)confinement in Yang-Mills-Chern-Simons theories in the maximal Abelian gauge
• Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries
• Conformal to Harmonic Gauge for Bosonic Strings
• Finite BRST-antiBRST Transformations for the Theories with Gauge Group
• Soft-Collinear Effective Theory: BRST Formulation
• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon
• Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau Gauge on the Lattice
• Comparative analysis of finite field-dependent BRST transformations
• Infrared propagators of Yang-Mills-Chern-Simons theories in linear covariant gauges
• Non-Abelian gauge theories with composite fields in the background field method
• On Consistent Lagrangian Quantization of Yang--Mills Theories without Gribov Copies
• On the consistency of Lorentz-Violating Yang-Mills theories: Gauge invariance and non-perturbative effects