In previous works, we have constructed a refined version of the Gribov-Zwanziger action in 4 dimensions, by taking into account a novel dynamical effect. In this paper, we explore the 3-dimensional case. Analogously to 4 dimensions, we obtain a ghost propagator behaving like 1/p(2) in the infrared, while the gluon propagator reaches a finite nonvanishing value at zero momentum. Simultaneously, a clear violation of positivity by the gluon propagator is also found. This behavior of the propagators turns out to be in agreement with the recent numerical simulations

So far, the infrared behavior of the gluon and ghost propagator based on the Gribov-Zwanziger approach predicted a positivity violating gluon propagator vanishing at zero momentum, and an infrared enhanced ghost propagator. However, recent data based on huge lattices have revealed a positivity violating gluon propagator which turns out to attain a finite nonvanishing value very close to zero momentum. At the same time the ghost propagator does not seem to be infrared enhanced anymore. We point out that these new features can be accounted for by yet unexploited dynamical effects within the Gribov-Zwanziger approach, leading to an infrared behavior in qualitatively good agreement with the new data.

Recent lattice data have reported an infrared suppressed, positivity violating gluon propagator which is nonvanishing at zero momentum and a ghost propagator which is no longer enhanced. This paper discusses how to obtain analytical results which are in qualitative agreement with these lattice data within the Gribov-Zwanziger framework. This framework allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gribov region. We elaborate to great extent on a previous short paper by presenting additional results, also confirmed by the numerical simulations. A detailed discussion on the soft breaking of the Becchi-Rouet-Stora-Tyutin symmetry arising in the Gribov-Zwanziger approach is provided.

The local composite operator A 2 µ is added to the Zwanziger action, which implements the restriction to the Gribov region Ω in Euclidean Yang-Mills theories in the Landau gauge. We prove that Zwanziger's action with the inclusion of the operator A 2 µ is renormalizable to all orders of perturbation theory, obeying the renormalization group equations. This allows to study the dimension two gluon condensate A 2 µ by the local composite operator formalism when the restriction to the Gribov region Ω is taken into account. The resulting effective action is evaluated at one-loop order in the MS scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to A 2 µ , but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without the inclusion of the condensate A 2 µ , are investigated. In particular, it is shown that in the original Gribov-Zwanziger formulation, i.e. without the inclusion of the operator A 2 µ , the resulting vacuum energy is always positive at oneloop order, independently from the choice of the renormalization scheme and scale. In the presence of A 2 µ , we are unable to come to a definite conclusion at the order considered. In the MS scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. Concerning the behaviour of the gluon and ghost propagators, we recover the well known consequences of the restriction to the Gribov region, and this in the presence of A 2 µ , i.e. an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. Such a behaviour is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.

In recent years, the Gribov-Zwanziger action was refined by taking into account certain dimension 2 condensates. In this fashion, one succeeded in bringing the gluon and the ghost propagator obtained from the GZ model in qualitative and quantitative agreement with the lattice data. In this paper, we shall elaborate further on this aspect. First, we shall show that more dimension 2 condensates can be taken into account than considered so far and, in addition, we shall give firm evidence that these condensates are in fact present by discussing the effective potential. It follows thus that the Gribov-Zwanziger action dynamically transforms itself into the refined version, thereby showing that the continuum nonperturbative Landau gauge fixing, as implemented by the Gribov-Zwanziger approach, is consistent with lattice simulations. * david.dudal@ugent.be † sorella@uerj.br ‡ nele.vandersickel@ugent.be arXiv:1105.3371v1 [hep-th]