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

A local and renormalizable framework for the gauge-invariant operator Amin⁡2A^2_{\min} in Euclidean Yang-Mills theories in linear covariant gauges

We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A^2_{\rm min}$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A^2_{\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A^2_{\rm min}$ turns out to be independent from the gauge parameter $\alpha$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.Comment: 35 pages; v2: ref. adde

The complex channel networks of bone structure

Bone structure in mammals involves a complex network of channels (Havers and Volkmann channels) required to nourish the bone marrow cells. This work describes how three-dimensional reconstructions of such systems can be obtained and represented in terms of complex networks. Three important findings are reported: (i) the fact that the channel branching density resembles a power law implies the existence of distribution hubs; (ii) the conditional node degree density indicates a clear tendency of connection between nodes with degrees 2 and 4; and (iii) the application of the recently introduced concept of hierarchical clustering coefficient allows the identification of typical scales of channel redistribution. A series of important biological insights is drawn and discussedComment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge

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.Comment: 19 pages, no figure

Some remarks on the spectral functions of the Abelian Higgs Model

We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model.Comment: 32 pages, 12 figure

More on the non-perturbative 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. 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.Comment: 15 pages, 1 figure; V2 typos fixed and inclusion of section on the ghost propagator. To appear in PhysRev

An exact nilpotent non-perturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge

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.Comment: 8 pages. v2: version accepted for publication in PhysRev

The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories

In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang-Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region $\Omega$ in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region $\Omega$ acquires a gauge independent meaning in the class of the physical correlators.Comment: 14 pages. v2: version accepted by Phys.Lett.