Aspects of the refined Gribov-Zwanziger action in linear covariant gauges

Abstract

We prove the renormalizability to all orders of a refined Gribov-Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the Faddeev-Popov operator is positive definite with respect to the transverse component of the gauge field, a procedure which turns out to be analogous to the restriction to the Gribov region in the Landau gauge. The model studied here can be regarded as the first approximation of a more general nonperturbative BRST invariant formulation of the refined Gribov-Zwanziger action in linear covariant gauges obtained recently in [Phys. Rev. D 92, no. 4, 045039 (2015) and arXiv:1605.02610 [hep-th]]. A key ingredient of the set up worked out in [Phys. Rev. D 92, no. 4, 045039 (2015) and arXiv:1605.02610 [hep-th]] is the introduction of a gauge invariant field configuration ${\mathbf{A}}_{\mu }$ which can be expressed as an infinite non-local series in the starting gauge field $A_{\mu }$. In the present case, we consider the approximation in which only the first term of the series representing ${\mathbf{A}}_{\mu }$ is considered, corresponding to a pure transverse gauge field. The all order renormalizability of the resulting action gives thus a strong evidence of the renormalizability of the aforementioned more general nonperturbative BRST invariant formulation of the Gribov horizon in linear covariant gauges.

arXiv comment26 pages, no figures, new references added

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• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
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• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Study of Gribov Copies in the Yang-Mills ensemble
• Constrained gauge-gravity duality in three and four dimensions
• Non-Abelian extension of the aether term and the Gribov problem
• Lorentz symmetry breaking in a Yang-Mills theory within the Gribov restriction
• An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• Predicting Planck scale and Newtonian constant from a Yang-Mills gauge theory: 1 and 2-loops estimates