Slavnov-Taylor constraints for non-trivial backgrounds

Abstract

We devise an algebraic procedure for the evaluation of Green's functions in SU(N) Yang-Mills theory in the presence of a non-trivial background field. In the ghost-free sector the dependence of the vertex functional on the background is shown to be uniquely determined by the Slavnov-Taylor identities in terms of a certain 1-PI correlator of the covariant derivatives of the ghost and the anti-ghost fields. At non-vanishing background this amplitude is shown to encode the quantum deformations to the tree-level background-quantum splitting. The approach only relies on the functional identities of the model (Slavnov-Taylor identities, $b$-equation, anti-ghost equation) and thus it is valid beyond perturbation theory, and in particular in a lattice implementation of the background field method. As an example of the formalism we analyze the ghost two-point function and the Kugo-Ojima function in an instanton background in SU(2) Yang-Mills theory, quantized in the background Landau gauge.

33 pages

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Cited by in corpus (13)

• Renormalization of gauge theories in the background-field approach
• AntiBRST symmetry and Background Field Method
• The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
• Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization
• Canonical Transformations and Renormalization Group Invariance in the presence of Non-trivial Backgrounds
• Background field method and the cohomology of renormalization
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Canonical Flow in the Space of Gauge Parameters
• The Stueckelberg Mechanism in the presence of Physical Scalar Resonances
• High-energy QCD evolution from BRST symmetry
• Some reference formulas for the generating functions of canonical transformations
• Non-trivial Backgrounds in (non-perturbative) Yang-Mills Theory by the Slavnov-Taylor Identity
• High-energy QCD evolution from Slavnov-Taylor identity