Gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: Taking into account the effects of the Gribov copies and of the dimension two condensates

Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, Ronaldo

doi:10.1103/physrevd.77.105023

Cited by 41 publications

(60 citation statements)

References 41 publications

(96 reference statements)

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“…Although being out of the aim of the present work, it is worth mentioning that a treatment of the Gribov issue similar to that of the Landau gauge [3,16] can be implemented in the maximal Abelian gauge, see for instance refs. [6,7,8,9,10]. Let us turn thus to the characterization of the zero modes of the Faddeev-Popov operator M ab , which clearly affect expression (19).…”

Section: The Gauge Fixing Conditionsmentioning

confidence: 99%

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Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

et al. 2014

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A study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU (2) and for different Euclidean space-time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: i) the finite Euclidean Yang-Mills action, ii) the finite Hilbert norm.

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Section: The Gauge Fixing Conditionsmentioning

confidence: 99%

“…On the other hand, the Hilbert norm A 2 is known to be deeply related to the Gribov issue. In fact, several properties of the Gribov region in both Landau and maximal Abelian gauge can be obtained by looking at all relative minima of A 2 along the gauge orbits, see [3,4,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

et al. 2014

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“…On the other hand, if we choose η = 1, we can see that, after some simple manipulations, the first equation of (34) reduces to ∇ ab = −∂ μ D ab μ − g f acb A c μ ∂ μ , which is exactly the purely off-diagonal components of the Faddeev-Popov operator for the Landau gauge. The second equation of (34) reduces to the second equation of (30). The third equation of (34) does not involve the interpolating parameter η, but once we choose η = 1, the first gauge condition of (32) turns out to be ∂ μ A a μ = 0, which means that we can substitute this in the third equation of (34) and obtain the same result for the Landau gauge (30).…”

Section: The Faddeev-popov Operator and Gribov Ambiguitiesmentioning

confidence: 68%

“…The LMAIG is then embedded into a larger class of gauges characterized by two gauge parameters (η and α ). See, for instance [34]. After renormalization, the original LMAIG is recovered by the limit α → 0.…”

Section: Gluon Propagatormentioning

confidence: 99%

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Gribov ambiguities at the Landau-maximal Abelian interpolating gauge

Pereira

Sobreiro

2014

Eur. Phys. J. C

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In a previous work, we presented a new method to account for the Gribov ambiguities in non-Abelian gauge theories. The method consists on the introduction of an extra constraint which directly eliminates the infinitesimal Gribov copies without the usual geometric approach. Such strategy allows one to treat gauges with non-hermitian FaddeevPopov operator. In this work, we apply this method to a gauge which interpolates among the Landau and maximal Abelian gauges. The result is a local and power counting renormalizable action, free of infinitesimal Gribov copies. Moreover, the interpolating tree-level gluon propagator is derived.

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On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions

Huber¹

2012

Springer Theses

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The infrared behavior of propagators and vertices is derived for the maximally Abelian gauge and the Gribov-Zwanziger action relying on functional equations. The derivation and analysis of Dyson-Schwinger equations increase considerably in complexity when going beyond the standard Landau gauge fixing and the available tools have to be improved. For the derivation of the equations a computer program (DoDSE ) was developed in order to handle the plethora of terms. The process of determining possible infrared solutions is abstracted to obtain further insight into the structure of the so-called infrared scaling solutions. It is found that a few simple steps suffice to determine possible infrared scaling relations directly from the action. This makes also complicated actions easily accessible.For the maximally Abelian gauge an infrared enhanced diagonal gluon propagator is found, while the off-diagonal degrees of freedom are infrared suppressed. This is in agreement with the idea of Abelian infrared dominance. Furthermore, it is proven that SU (2) and higher SU (N ) have the same infrared behavior, although the corresponding actions differ. Under a suitable truncation the Dyson-Schwinger equations are solved in the deep infrared to obtain values for the exponents of the power laws. The maximally Abelian gauge constitutes the first instance where a consistent scaling solution was found besides the Landau gauge.Restricting the integration in field configuration space to the Gribov region of the Landau gauge with the Gribov-Zwanziger action leads to two solutions qualitatively equivalent to the one obtained with the standard Faddeev-Popov gauge fixing. In both cases the gluon propagator is infrared suppressed and the infrared enhanced ghost propagator For further investigations of Yang-Mills theory the possibility to derive Dyson-Schwinger equations with the computer will prove useful. The presented method for determining possible infrared scaling solutions will also alleviate their analyses.

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Gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: Taking into account the effects of the Gribov copies and of the dimension two condensates

Cited by 41 publications

References 41 publications

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

Gribov ambiguities at the Landau-maximal Abelian interpolating gauge

On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions

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