Propagators and running coupling from SU(2) lattice gauge theory

Bloch, Jacques; Cucchieri, Attilio; Langfeld, Kurt; Mendes, Tereza

doi:10.1016/j.nuclphysb.2004.03.021

Cited by 120 publications

(207 citation statements)

References 60 publications

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“…[49] for the SU (2) group in four dimensions (see also Ref. [26]), then our value of β corresponds to β ≈ 2.21 in the four dimensional case. In this work we did not do a systematic study of Gribov-copy effects [24,50,51,52,53,54,55,56,57] for the two propagators, since here we are interested in possible systematic effects due to the use of asymmetric lattices.…”

Section: Simulationsmentioning

confidence: 55%

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Infrared behavior of gluon and ghost propagators from asymmetric lattices

Cucchieri

Mendes

2006

Phys. Rev. D

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We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU (2) gauge theory. Data have been obtained using asymmetric lattices (V = 20 2 ×60, 40 2 ×60, 8 2 × 64, 8 2 × 140, 12 2 × 140 and 16 2 × 140) for the lattice coupling β = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V . By comparing these results with data obtained using symmetric lattices (V = 60 3 and 140 3 ), we find that both propagators suffer from systematic effects in the infrared region (p 650MeV). In particular, the gluon (respec. ghost) propagator is less IR-suppressed (respec. enhanced) than in the symmetric case. We discuss possible implications of the use of asymmetric lattices.

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Section: Simulationsmentioning

confidence: 55%

“…Numerical studies of lattice gauge theories confirm the IR divergence of the Landau ghost propagator [23,24,25,26] and have now also established that the Landau gluon propagator shows a turnover in the IR region, attaining a finite value for p ≈ 0. (A reliable extrapolation of D(0) to the infinite-volume limit is still lacking [18].)…”

Section: Introductionmentioning

confidence: 79%

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Cucchieri

Mendes

2006

Phys. Rev. D

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“…While early lattice studies of those propagators [32,33] supported the predicted infrared behavior based on their DysonSchwinger equations qualitatively well [34,35], small but significant differences are increasingly being observed nowadays in detailed comparisons and studies of finitevolume effects [36][37][38][39][40]. In particular, as a result of these differences, the Kugo-Ojima confinement criterion of local quantum field theory is now frequently stated to be violated in the infinite-volume limit:…”

Section: Discussionmentioning

confidence: 99%

Decontracted double BRST symmetry on the lattice

2008

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We present the Curci-Ferrari model on the lattice. In the massless case the topological interpretation of this model with its double BRST symmetry relates to the Neuberger 0/0 problem which we extend to include the ghost/anti-ghost symmetric formulation of the non-linear covariant Curci-Ferrari gauges on the lattice. The introduction of a Curci-Ferrari mass term, however, serves to regulate the 0/0 indeterminate form of physical observables observed by Neuberger. While such a mass m decontracts the double BRST/anti-BRST algebra, which is well-known to result in a loss of unitarity, observables can be meaningfully defined in the limit m → 0 via l'Hospital's rule. At finite m the topological nature of the partition function used as the gauge fixing device seems lost. We discuss the gauge parameter ξ and mass m dependence of the model and show how both cancel when m ≡ m(ξ) is appropriately adjusted with ξ.

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“…Of particular relevance in such a study is the nature of the gluon-ghost vertices involved; in fact, in the PT-BFM scheme there will be two such vertices: IΓ ν , appearing in figure 3, and IΓ β , which will appear in the SD equation for the ghost propagator. The IR behavior of IΓ β (in the Landau gauge) is currently under investigation on the lattice [74]; it would clearly be important to settle the issue of whether it is divergent or finite.…”

Section: Jhep12(2006)012mentioning

confidence: 99%

Gluon mass generation in the PT-BFM scheme

Aguilar

Papavassiliou

2006

J. High Energy Phys.

193

316

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In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-byorder in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed.

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Propagators and running coupling from SU(2) lattice gauge theory

Cited by 120 publications

References 60 publications

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Decontracted double BRST symmetry on the lattice

Gluon mass generation in the PT-BFM scheme

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