Sp Sorella

New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach

So far, the infrared behavior of the gluon and ghost propagat or based on the Gribov-Zwanziger approach predicted a positivity violating gluon propagator vanishing a t zero momentum, and an infrared enhanced ghost propagator. However, recent data based on huge lattices hav revealed a positivity violating gluon propagator which turns out to attain a finite nonvanishingvalue 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.

The anomalous dimension of the composite operator A(2) in the Landau gauge

Abstract The local composite operator A 2 is analysed in pure Yang–Mills theory in the Landau gauge within the algebraic renormalization. It is proven that the anomalous dimension of A 2 is not an independent parameter, being expressed as a linear combination of the gauge β function and of the anomalous dimension of the gauge fields.

Analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate , which has attracted much attention in the Landau gauge.

Gluon–ghost condensate of mass dimension 2 in the Curci–Ferrari gauge

Abstract The effective potential for an on-shell BRST invariant gluon–ghost condensate of mass dimension 2 in the Curci–Ferrari gauge in SU(N) Yang–Mills is analysed by combining the local composite operator technique with the algebraic renormalization. We pay attention to the gauge parameter independence of the vacuum energy obtained in the considered framework and discuss the Landau gauge as an interesting special case.

Renormalizability of the local composite operator Aμ2 in linear covariant gauges

Abstract The local composite operator A μ 2 is analysed within the algebraic renormalization in Yang–Mills theories in linear covariant gauges. We establish that it is multiplicatively renormalizable to all orders of perturbation theory. Its anomalous dimension is computed to two-loops in the MS scheme.

Exact nilpotent nonperturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge

We point out the existence of a nonperturbative 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.

An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions

Abstract The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev–Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU ( N ) Yang–Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribovʼs no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanzigerʼs horizon function. The action allowing to implement this condition is the Gribov–Zwanziger action. This establishes in a precise way the equivalence between Gribovʼs no-pole condition and Zwanzigerʼs horizon condition.

Gribov horizon in the presence of dynamical mass generation in euclidean Yang-Mills theories in the Landau gauge

Abstract The infrared behavior of the gluon and ghost propagators is analyzed in Yang–Mills theories in the presence of dynamical mass generation in the Landau gauge. By restricting the domain of integration in the path-integral to the Gribov region Ω , the gauge propagator is found to be suppressed in the infrared, while the ghost propagator is enhanced.

More on the nonperturbative Gribov-Zwanziger quantization of linear covariant gauges

In this paper, we discuss the gluon propagator in the linear covariant gauges in D = 2, 3, 4 Euclidean dimensions. Nonperturbative 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) behavior, 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 nonperturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our nonperturbative definition of the linear covariant gauge.

Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST-invariant two-point correlation function

In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations A(h). Such configurations can be obtained through the minimization of the functional A(min)(2) along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter alpha entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use to probe the pole structure of the massive gauge boson in a gauge-invariant fashion.