More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges

Abstract

In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into account via the so-called Refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon propagator displays a massive (decoupling) behaviour, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced non-perturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our non-perturbative definition of the linear covariant gauge.

15 pages, 1 figure; V2 typos fixed and inclusion of section on the ghost propagator. To appear in PhysRev D

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• The ghost-gluon vertex in the presence of the Gribov horizon
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• Some remarks on the spectral functions of the Abelian Higgs Model
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• Faddeev-Popov Matrix in Linear Covariant Gauge: First Results
• On a renormalizable class of gauge fixings for the gauge invariant operator $A_{\min }^2$
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• Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
• Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory
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• Exploring new horizons of the Gribov problem in Yang-Mills theories
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• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• Implications of the Topological Chern-Simons mass in the Gap Equation
• Gauge copies and the fate of background independence in Yang-Mills theories: a leading order analysis
• Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau Gauge on the Lattice
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• On the consistency of Lorentz-Violating Yang-Mills theories: Gauge invariance and non-perturbative effects