The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

The local composite operator A^2 is added to the Zwanziger action, which implements the restriction to the Gribov region in Euclidean Yang-Mills theories in the Landau gauge. We prove the renormalizability of this action to all orders of perturbation theory. This allows to study the dimension two gluon condensate by the local composite operator formalism when the restriction is taken into account. The effective action is evaluated at one-loop order in the MSbar scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to , 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 , are investigated. It is shown that in the original Gribov-Zwanziger formulation (without ), the vacuum energy is always positive at 1-loop order, independently from the renormalization scheme and scale. With , we are unable to come to a definite conclusion at the order considered. In the MSbar 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. We recover the well known consequences of the restriction, and this in the presence of : an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. This behaviour is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.Comment: 42 pages, 10 .eps figures. v2: Version accepted for publication in Phys.Rev.D. Added references. Technical details have been collected in two appendice

Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate ⟨A2⟩\braket{A^2} in the Landau gauge

We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $\braket{A^2}$. Including this effect allows to obtain an acceptable fit up to 1 \'{a} 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate $D(0)=8.3\pm0.5\text{GeV}^{-2}$. As a byproduct, we can also provide the prediction $\braket{g^2 A^2}\approx 3\text{GeV}^2$ obtained at the renormalization scale $\mu=10\text{GeV}$.Comment: 17 pages, 10 figures, updated version, accepted for publication in Phs.Rev.

An Infrared Safe perturbative approach to Yang-Mills correlators

We investigate the 2-point correlation functions of Yang-Mills theory in the Landau gauge by means of a massive extension of the Faddeev-Popov action. This model is based on some phenomenological arguments and constraints on the ultraviolet behavior of the theory. We show that the running coupling constant remains finite at all energy scales (no Landau pole) for $d>2$ and argue that the relevant parameter of perturbation theory is significantly smaller than 1 at all energies. Perturbative results at low orders are therefore expected to be satisfactory and we indeed find a very good agreement between 1-loop correlation functions and the lattice simulations, in 3 and 4 dimensions. Dimension 2 is shown to play the role of an upper critical dimension, which explains why the lattice predictions are qualitatively different from those in higher dimensions.Comment: 16 pages, 7 figures, accepted for publication in PR

A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories

The Gribov copies and their consequences on the infrared behavior of the gluon propagator are investigated in Euclidean Yang-Mills theories quantized in linear covariant gauges. Considering small values of the gauge parameter, it turns out that the transverse component of the gluon propagator is suppressed, while its longitudinal part is left unchanged. A Green function, G_{tr}, which displays infrared enhancement and which reduces to the ghost propagator in the Landau gauge is identified. The inclusion of the dimension two gluon condensate is also considered. In this case, the transverse component of the gluon propagator and the Green function G_{tr} remain suppressed and enhanced, respectively. Moreover, the longitudinal part of the gluon propagator becomes suppressed. A comparison with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations is provided.Comment: 20 page

Poisson homology of r-matrix type orbits I: example of computation

In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. Then we describe the $r$-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or $CP^n$-type orbits of $SL(n,C)$. Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on $CP^n$-type orbits. In Section 2 we calculate the Poisson homology of Drinfeld--Sklyanin Poisson brackets which belong to the $r$-matrix Poisson family

A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results

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 BRST symmetry arising in the Gribov-Zwanziger approach is provided.Comment: 38 pages, 9 figures, the content of section V has been extended and adapte

A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions

Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for publication in the EPJ

The ice-limit of Coulomb gauge Yang-Mills theory

In this paper we describe gauge invariant multi-quark states generalising the path integral framework developed by Parrinello, Jona-Lasinio and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice-limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is llustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark--antiquark potential.Comment: 25 pages, 4 figure

Dimension two gluon condensates in a variety of gauges and a gauge invariant Yang-Mills action with a mass

We give a short overview of our work concerning the dimension two operator A^2 in the Landau gauge and its generalizations to other gauges. We conclude by discussing recent work that leads to a renormalizable gauge invariant action containing a mass parameter, based on the operator F 1/D^2 F.Comment: 4 pages. espcrc2.sty is used. Talk given at "13th International Conference In QCD (QCD 06), 3-7 Jul 2006, Montpellier, France

Landau gauge within the Gribov horizon

We consider a model which effectively restricts the functional integral of Yang--Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as ordinary Yang Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the $BRS$ symmetry.Comment: 17 pages, NYU-TH-93/10/0