On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

Alkofer, Reinhard; Huber, Markus Q.; Mader, Valentin; Windisch, Andreas

doi:10.22323/1.136.0003

Cited by 12 publications

(10 citation statements)

References 70 publications

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“…The hypothesis of Abelian dominance [45] states that the Cartan gluons dominate long-range interactions. This has been observed in lattice simulations [46,47] and is also corroborated by an infrared analysis of the functional equations [48,49]. Fur-thermore, the Cartan gluons also dominate at large momenta [50,51].…”

Section: Introductionsupporting

confidence: 57%

Infrared saturation and phases of gauge theories with BRST symmetry

et al. 2014

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We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation of the transverse equation of motion of the gauge boson at low momenta in the Higgs phase, while the saturation is entirely due to unphysical degrees of freedom in the confining phase. This corollary to the Kugo–Ojima confinement criterion in linear covariant gauges also is sufficient for confinement in general covariant gauges with BRST and anti-BRST symmetry, maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb gauge and in the Gribov–Zwanziger theory.

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Section: Introductionsupporting

confidence: 57%

Infrared saturation and phases of gauge theories with BRST symmetry

et al. 2014

Self Cite

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“…And, in addition to lattice calculations in this gauge (see e.g. [13] and references therein), also the functional equations are a subject of current investigations [14,15]. This will allow further insight into the conjecture of Abelian dominance and, in the best of all cases, into the importance of chromomagnetic degrees of freedom as e.g.…”

Section: A Remark On Suitable Gaugesmentioning

confidence: 94%

Panel discussion: What don’t we know about confinement?

Alkofer

Diakonov

Pawlowski

et al. 2011

AIP Conference Proceedings

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Abstract. The participants in this discussion session of the QCHS 9 meeting were each asked the following question: "What would be the most useful piece of information that you could obtain, by whatever means, that would advance your own program, and/or our general understanding of confinement?" This proceedings contains a brief summary of each panel member's contribution to the discussion, provided by the panel members themselves.

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“…Other studies concerning scaling behaviour of the Yang-Mills system in gauges different to Landau gauge have been performed, such as ghost-antighost symmetric gauges [35], maximally Abelian gauges [36,37] and interpolating gauges [38]. Similarly, linear covariant gauges have also been investigated on the lattice [39,40].…”

Section: Tt Tmentioning

confidence: 99%

Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

Llanes-Estrada

Williams

2012

Phys. Rev. D

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Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for high (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as "scaling" features an infrared power law for the gluon and ghost propagators, the "massive" solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quantization. What we find, in four dimensions and in a rainbow approximation, is that stochastic quantization supports both solutions in Landau gauge but the scaling solution abruptly disappears when the parameter controlling the drift force is separated from zero (soft gauge-fixing), recovering only the perturbative propagators; the massive solution seems to survive the extension outside Landau gauge. These results are consistent with the scaling solution being related to the existence of a Gribov horizon, with the massive one being more general. We also examine the effective action in Faddeev-Popov quantization that generates the rainbow and we find, for a bare vertex approximation, that the the massive-type solutions minimise the quantum effective action.

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On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

Cited by 12 publications

References 70 publications

Infrared saturation and phases of gauge theories with BRST symmetry

Infrared saturation and phases of gauge theories with BRST symmetry

Panel discussion: What don’t we know about confinement?

Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

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