Non-Abelian gauge theories with composite fields in the background field method

Abstract

Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green's functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional of vertex Green's functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and utilized on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background.On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov--Zwanziger theory, including the case of a local BRST-invariant horizon, and by the Volovich--Katanaev model of two-dimensional gravity with dynamical torsion.

arXiv comment42 pages, presentation improved, references added, summary improved, version accepted for publication in Universe

References in corpus (41)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• An exact nilpotent non-perturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge
• Stability and renormalization of Yang-Mills theory with Background Field Method: a regularization independent proof
• A local and BRST-invariant Yang-Mills theory within the Gribov horizon
• Renormalization of gauge theories in the background-field approach
• On the Functional Renormalization Group approach for Yang-Mills fields
• Gribov horizon beyond the Landau gauge
• Is soft breaking of BRST symmetry consistent?
• Field-dependent BRST transformations in Yang-Mills theory
• The Power of Duality -- Exact Results in 4D SUSY Field Theory
• Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories
• Exact Adler Function in Supersymmetric QCD
• Further comments on the background field method and gauge invariant effective actions
• Field dependent nilpotent symmetry for gauge theories
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• Functional renormalization group approach and gauge dependence in gravity theories
• Derivation of the exact expression for the D function in N=1 SQCD
• Algebraic Aspects of the Background Field Method
• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• The Background Field Method as a Canonical Transformation
• Finite BRST-antiBRST Transformations in Lagrangian Formalism
• Soft breaking of BRST symmetry and gauge dependence
• Background gauge renormalization and BRST identities
• A systematic study of finite BRST-BV transformations in field-antifield formalism
• Comments on interactions in the SUSY models
• Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model
• Legendre transformations and Clairaut-type equations
• Field-Dependent BRST-antiBRST Lagrangian Transformations
• Multiplicative renormalization of Yang-Mills theories in the background-field formalism
• Effective Action of Composite Fields for General Gauge Theories in BLT-Covariant Formalism
• The nilpotent "BRST" symmetry for the Gribov-Zwanziger theory
• Loop expansion of the average effective action in the functional renormalization group approach
• On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry
• The Gribov problem in presence of background field for $SU(2)$ Yang-Mills theory
• Renormalization of six-dimensional Yang-Mills theory in a background gauge field
• On Composite fields approach to Gribov copies elimination in Yang-Mills theories
• Renormalizability of $\mathcal{N}=1$ super Yang-Mills theory in Landau gauge with a Stueckelberg-like field
• Quantization of Two-Dimensional Gravity with Dynamical Torsion
• Study of a gauge invariant local composite fermionic field
• Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries
• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon

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