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Register a new userAn exact nilpotent non-perturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge
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We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.
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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.
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.
The Refined Gribov-Zwanziger framework takes into account the existence of equivalent gauge field configurations in the gauge-fixing quantization procedure of Euclidean Yang-Mills theories. Recently, this setup was extended to the family of linear covariant gauges giving rise to a local and BRST-invariant action. In this paper, we give an algebraic proof of the renormalizability of the resulting action to all orders in perturbation theory.
We introduce, within the Refined-Gribov-Zwanziger setup, a composite BRST invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behaviour of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure.
The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N=1 Super Yang--Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N=1 Super Yang--Mills theories, namely: the existence of the gluino condensate as well as the vanishing of the vacuum energy.
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