Lattice gauge fields topology uncovered by quaternionic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>-model embedding

Gubarev, F. V.; Morozov, S. M.

doi:10.1103/physrevd.72.076008

Cited by 9 publications

(60 citation statements)

References 71 publications

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“…As far as the topological density q 2 and HP 1 -projected action density s are concerned, their construction is fully described in Refs. [18,19] and will not be repeated here. The prime objects of our study are the dimensionless quantities…”

Section: Observables and Theoretical Expectationsmentioning

confidence: 99%

“…First, the heavy quark potential extracted from HP 1 -projected Wilson loops ( Figure 9 in the second paper of Ref. [18]) appears to be concave at distances |x| 4 (lattice units) for gauge configurations thermalized at bare coupling β = 2.60. Secondly, the HP 1 -based topological density correlation function q 0 q x reveals a positive core at small distances, the size of which scales in physical units [19].…”

Section: For Details)mentioning

confidence: 99%

“…[18,19]. The most straightforward way to introduce the idea of the method is to consider first Yang-Mills theory with gauge group SU (2) (group of unit quaternions) in the limit, in which the gauge potentials A µ are smooth functions of space-time coordinates.…”

Section: Review Of Hpmentioning

confidence: 99%

“…What is even more important is that near the continuum limit the HP 1 -projected fields capture the majority of non-perturbative aspects of SU (2) Yang-Mills theory and reproduce, for instance, the full tension of the confining string and (quenched) quark condensate (see Refs. [18,19] for further details). Being numerically superior, the HP 1 embedding approach is naturally our method of choice to investigate the topological aspects of the confining string and to study its geometrical properties.…”

Section: Introductionmentioning

confidence: 99%

“…It is known [16] that the full tower of eigenmodes indeed reproduces ∼ 1/a 8 behavior, while the restriction to lowest eigenvalues [17] introduces explicit and a priori ambiguous cut on the leading singularity. Therefore the essentially unique alternative construction which fits the above requirements is HP 1 σ-model embedding approach [18,19] which is to be reviewed in Section II. Here we only mention that this method indeed provides parameter free definition of the topological density in which the leading power divergence is removed.…”

Section: Introductionmentioning

confidence: 99%

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Confining string and its widening inHP1embedding approach

Chernodub

Gubarev

2007

Phys. Rev. D

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Structure of confining string in terms of the topological charge density and the action density is studied in SU (2) Yang-Mills theory on the lattice using HP 1 σ-model embedding approach. We find that the confining flux tube noticeably suppresses both the topological charge and the action densities. Beyond the string formation length the string cross section in terms of these quantities is well described by a Gaussian profile. In both cases the squared string width is found to be a logarithmic function of the string length confirming the Lüscher widening of the chromoelectric string. Characteristic string scales in terms of the topological and action densities are estimated as well.

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Section: Observables and Theoretical Expectationsmentioning

confidence: 99%

Section: For Details)mentioning

confidence: 99%

Section: Review Of Hpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Confining string and its widening inHP1embedding approach

Chernodub

Gubarev

2007

Phys. Rev. D

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On topological properties of vacuum defects in lattice Yang–Mills theories

et al. 2007

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We study correlations between low-lying modes of the overlap Dirac operator and vacuum defects, center vortices and three-dimensional volumes, in lattice SU(2) gluodynamics. The low-lying modes are apparently sensitive to topological properties of the underlying gluon field configurations while the vacuum defects are crucial for the confinement. We find distinct positive correlation in both cases. In case of vortices the correlation is stronger.

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Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

et al. 2005

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The local composite operator A 2 µ is added to the Zwanziger action, which implements the restriction to the Gribov region Ω in Euclidean Yang-Mills theories in the Landau gauge. We prove that Zwanziger's action with the inclusion of the operator A 2 µ is renormalizable to all orders of perturbation theory, obeying the renormalization group equations. This allows to study the dimension two gluon condensate A 2 µ by the local composite operator formalism when the restriction to the Gribov region Ω is taken into account. The resulting effective action is evaluated at one-loop order in the MS scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to A 2 µ , but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without the inclusion of the condensate A 2 µ , are investigated. In particular, it is shown that in the original Gribov-Zwanziger formulation, i.e. without the inclusion of the operator A 2 µ , the resulting vacuum energy is always positive at oneloop order, independently from the choice of the renormalization scheme and scale. In the presence of A 2 µ , we are unable to come to a definite conclusion at the order considered. In the MS scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. Concerning the behaviour of the gluon and ghost propagators, we recover the well known consequences of the restriction to the Gribov region, and this in the presence of A 2 µ , i.e. an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. Such a behaviour is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.

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Lattice gauge fields topology uncovered by quaternionicσ-model embedding

Cited by 9 publications

References 71 publications

Confining string and its widening inHP1embedding approach

Confining string and its widening inHP1embedding approach

On topological properties of vacuum defects in lattice Yang–Mills theories

Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

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