Renormalizability of the refined Gribov-Zwanziger action in linear covariant gauges

Capri, M. A. L.; Fiorentini, D.; Pereira, Antônio D.; Sorella, S. P.

doi:10.1103/physrevd.96.054022

Cited by 43 publications

(107 citation statements)

References 80 publications

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“…This was achieved by the introduction of the suitable gauge-invariant fields A h , φ h and ψ h , see [1][2][3][4][5], which, albeit local, are non-polynomial in the auxiliary Stueckelberg-type field ξ a . Nevertheless, such variables as well as the proposed non-perturbative matter coupling give rise to a local ation which can be proven to be renormalizable to all orders, see [70,81].…”

Section: Discussionmentioning

confidence: 99%

“…(67), in both gauges is the same. Therefore, the scalar field action non-perturbatively coupled to the gauge sector is given by (70). Clearly, at first order, all the computations presented in this section remain valid for the Curci-Ferrari gauges, namely, the calculation of the vacuum energy and of the scalar field propagator.…”

Section: Linear Covariant and Curci-ferrari Gaugesmentioning

confidence: 99%

“…The local action turns out to be renormalizable to all orders in perturbation theory [70], while implementing the restriction of the domain of integration in the path integral to a region free from a large set of Gribov copies in the linear covariant gauges in a BRST-invariant way. Such a feature allows for a well-defined Slavnov-Taylor identity, through which the gauge parameter independence of gauge-invariant correlation functions can be established.…”

Section: A Hmentioning

confidence: 99%

“…Furthermore, in the case of d = 2, due to the absence of condensates, the action remains the original one given by Eq. (70).…”

Section: Linear Covariant and Curci-ferrari Gaugesmentioning

confidence: 99%

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A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

et al. 2017

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In this work, we study the propagators of matter fields within the framework of the refined GribovZwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the FaddeevPopov operator is added in the matter sector.

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Section: Discussionmentioning

confidence: 99%

Section: Linear Covariant and Curci-ferrari Gaugesmentioning

confidence: 99%

Section: A Hmentioning

confidence: 99%

“…Furthermore, in the case of d = 2, due to the absence of condensates, the action remains the original one given by Eq. (70).…”

Section: Linear Covariant and Curci-ferrari Gaugesmentioning

confidence: 99%

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A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

et al. 2017

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“…In the present work, we have pursued the previous investigation started in [31,32] The main result obtained is that the starting action Σ in presence of the gauge invariant composite operators (ψ h ,ψ h ) is renormalizable to all orders in perturbation theory.…”

Section: Discussionmentioning

confidence: 99%

Study of a gauge invariant local composite fermionic field

2020

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In this work, we study a gauge invariant local non-polynomial composite spinor field in the fundamental representation in order to establish its renormalizability. Similar studies were already done in the case of pure Yang-Mills theories where a local composite gauge invariant vector field was obtained and an invariant renormalizable mass term could be introduced. Our model consists of a massive Euclidean Yang-Mills action with gauge group SU (N ) coupled to fermionic matter in the presence of an invariant spinor composite field and quantized in the linear covariant gauges. The whole set of Ward identities is analysed and the algebraic proof of the renormalizability of the model is obtained to all orders in a loop expansion. I. INTRODUCTIONThe theoretical studies of quantum chromodynamics (QCD) in the low energy regime, where nonperturbative phenomena like confinement take place, still lack a satisfactory understanding.Besides quark confinement, let us underline that the gluon confinement is still a challenging, yet unsolved, issue. Several nonperturbative techniques based on the studies of the Dyson-Schwinger equations, functional renormalization group, Kugo-Ojima criterion, Gribov-Zwanziger approach and its refined version, have provided a fruitful ground for a better understanding of the behaviour of the two-point Landau gauge gluon correlation function in the infrared region, see . The output of these investigations is in quite good agreement with the lattice data on the gluon propagator, which exhibit a violation of the reflection positivity [26][27][28][29][30]. This peculiar behaviour of the gluon propagator is commonly interpreted as a signal of gluon confinement, due to the impossibility of attaching a physical meaning to the gluon as an excitation of the spectrum of the theory.

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On a renormalizable class of gauge fixings for the gauge invariant operatorAmin2

et al. 2018

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The dimension two gauge invariant non-local operator A 2 min , obtained through the minimization of d 4 xA 2 along the gauge orbit, allows to introduce a non-local gauge invariant configuration A h µ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both A 2 min and A h µ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of A 2 min gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's R ζ -gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field. *

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Renormalizability of the refined Gribov-Zwanziger action in linear covariant gauges

Cited by 43 publications

References 80 publications

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

Study of a gauge invariant local composite fermionic field

On a renormalizable class of gauge fixings for the gauge invariant operatorAmin2

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