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.

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

References in corpus (13)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Exact Adler Function in Supersymmetric QCD
• 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
• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• Finite BRST-antiBRST Transformations in Lagrangian Formalism
• A systematic study of finite BRST-BV transformations in field-antifield formalism
• Comments on interactions in the SUSY models
• Field-Dependent BRST-antiBRST Lagrangian Transformations
• The nilpotent "BRST" symmetry for the Gribov-Zwanziger theory
• The Gribov problem in presence of background field for $SU(2)$ Yang-Mills theory
• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon

Cited by in corpus (1)

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