Gauge fixing and the gluon propagator in renormalizable xi gauges

Bicudo, Pedro; Binosi, Daniele; Cardoso, Nuno; Oliveira, Orlando; Silva, Paulo

doi:10.22323/1.251.0317

Cited by 4 publications

(7 citation statements)

References 45 publications

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“…It can be shown, [43], that the longitudinal form factor remains bare, as is usual in the linear covariant gauge. This fact is also confirmed non-perturbatively using lattice simulations [69,75] and is consistent with the findings in [35,39] as well.…”

Section: Refined Gribov-zwanziger Actionsupporting

confidence: 90%

The BRST-invariant vacuum state of the Gribov–Zwanziger theory

et al. 2019

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We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the effective potential, showing the emergence of BRST-invariant dimension 2 condensates stabilizing the vacuum. This paper sets the stage at zero temperature, and clears the way to studying the Gribov-Zwanziger gap equations, and particularly the horizon condition, at finite temperature in future work. I. INTRODUCTIONUp until now, quark and gluon confinement has not been rigorously proven. It is well known that the perturbative formalism fails for non-Abelian gauge theories at low energy, since the coupling constant g 2 is strong. To get reliable results in the infrared (IR) in the continuum formulation, non-perturbative methods are needed. For an overview of such methods and obtained results, let us refer for example to . Notice that the continuum formulation requires gauge fixing, in which case lattice analogues of dedicated gauge fixings can be a powerful ally giving complementary insights, see for some relevant works in this area.Motivated by this, a number of studies over the past decade have focused on the gluon, quark and also ghost propagator in the infrared region, where color degrees of freedom are confined. Although these objects are unphysical by themselves -being gauge variant -they are nevertheless the basic building blocks, next to the interaction vertices, entering gauge-invariant objects directly linked to physically relevant quantities such as the spectrum, decay constants, critical exponents and temperatures, etc.One particular way to deal with non-perturbative physics at the level of elementary degrees of freedom is by dealing with the Gribov issue [21,80]: the fact that there is no unique way of selecting one representative configuration of a given gauge orbit in covariant gauges [81]. As there is also no rigourous way to deal properly with the existence of gauge copy modes in the path integral quantization procedure, in this paper we will use a well-tested formalism available to deal with the issue, which is known as the Gribov-Zwanziger (GZ) formalism: a restriction of the path integral to a smaller subdomain of gauge fields [80,82,83].This approach was first proposed for the Landau and the Coulomb gauges . It long suffered from a serious drawback: its concrete implementation seemed to be inconsistent with BRST (Becchi-Rouet-Stora-Tyutin [84-86]) invariance of the gauge-fixed theory, which clouded its interpretation as a gauge (fixed) theory. Only more recently was it realized by some of us and colleagues how to overcome this complication to get a BRST-invariant restriction of the gauge path integral . As a bonus, the method also allowed the generalization of the GZ approach to the linear covariant gauges, amongst others [36,37,43,45].Another issue with the original GZ approach was that some of its major leading-order predictions did not match the corresponding lattice output. Indeed, in the case of the...

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Section: Refined Gribov-zwanziger Actionsupporting

confidence: 90%

The BRST-invariant vacuum state of the Gribov–Zwanziger theory

et al. 2019

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“…[96,97]. In addition, although we focused on the Landau gauge case throughout this discussion, recent lattice simulations [98] and a variety of analytic studies [99][100][101][102] have indicated that gluon propagators continue to saturate in the infrared region for values of the gauge-fixing parameter that are at least within the [0, 0.5] interval.…”

Section: Discussionmentioning

confidence: 99%

The gluon mass generation mechanism: A concise primer

2016

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We present a pedagogical overview of the nonperturbative mechanism that endows gluons with a dynamical mass. This analysis is performed based on pure Yang-Mills theories in the Landau gauge, within the theoretical framework that emerges from the combination of the pinch technique with the background field method. In particular, we concentrate on the Schwinger-Dyson equation satisfied by the gluon propagator and examine the necessary conditions for obtaining finite solutions within the infrared region. The role of seagull diagrams receives particular attention, as do the identities that enforce the cancellation of all potential quadratic divergences. We stress the necessity of introducing nonperturbative massless poles in the fully dressed vertices of the theory in order to trigger the Schwinger mechanism, and explain in detail the instrumental role of these poles in maintaining the Becchi-Rouet-Stora-Tyutin symmetry at every step of the mass-generating procedure. The dynamical equation governing the evolution of the gluon mass is derived, and its solutions are determined numerically following implementation of a set of simplifying assumptions. The obtained mass function is positive definite, and exhibits a power law running that is consistent with general arguments based on the operator product expansion in the ultraviolet region. A possible connection between confinement and the presence of an inflection point in the gluon propagator is briefly discussed.

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“…For the moment, numerical simulations have focused on the implementation of the LCG on the lattice [5,6,7,8] and on the study of the gluon propagator [7,9,10]. On the other hand, it is still an open problem how to define the Faddeev-Popov (FP) matrix for LCG on the lattice.…”

Section: Why Study the Linear Covariant Gauge On The Lattice?mentioning

confidence: 99%

“…A few numerical studies of the gluon propagator have been carried out, using the above lattice formulation for LCG [7,9]. In particular, it has been checked, for the SU(2) and SU(3) gauge groups, that the longitudinal propagator D l (p 2 ) satisfies the relation p 2 D l (p 2 ) = ξ , as predicted by perturbation theory.…”

Section: )mentioning

confidence: 99%