Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance

Huber, Markus Q.; Alkofer, Reinhard; Schwenzer, Kai

doi:10.48550/arxiv.1103.0236

Cited by 4 publications

(5 citation statements)

References 25 publications

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“…In the recent study [20] almost perfect Abelian dominance of the string tension on large physical volumes in quenched SU(3) has been found. Complementary to the lattice approach, Abelian dominance has been analyzed perturbatively [21,22] and in Dyson-Schwinger and renormalization group equation studies [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

Schröck

Vogt

2016

Phys. Rev. D

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Functional equations like exact renormalisation group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. In the maximally Abelian gauge first results have been obtained which are very encouraging because Abelian infrared dominance has been found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. It is demonstrated how the two solutions are related in the maximally Abelian gauge. As in all two-point Dyson-Schwinger equations of the MAG the infrared dominant diagrams are sunset diagrams, in addition, a BPHZ regularisation and renormalisation of a test system with a sunset-like diagram is presented.

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Section: Introductionmentioning

confidence: 99%

Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

Schröck

Vogt

2016

Phys. Rev. D

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“…It would be also interesting to extend the current study to other covariant gauges like the maximally Abelian gauge. There, direct calculations are complicated due to its IR dominant two-loop diagrams [25,84].…”

Section: Resultsmentioning

confidence: 99%

Yang-Mills propagators in linear covariant gauges from Nielsen identities

Napetschnig,

Alkofer,

Huber

et al. 2021

Preprint

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We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilise Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter 0 < ξ ≤ 5. Extrapolating the propagators to ξ → ∞ we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values ξ 1/2 of the gauge fixing parameter. It is shown that the correlation functions, and in particular the ghost propagator, change significantly with increasing gauge parameter. In turn, the ghost-gluon running coupling as well as the position of the zero crossing of the Schwinger function of the gluon propagator remain within the uncertainties of our calculation unchanged.

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“…In DSEs they come in two types called sunset and squint diagrams, see App. B. Analytically, the importance of two-loop diagrams in the non-perturbative regime was analyzed for the scaling type of solutions in the Landau gauge [131,304,307,[383][384][385] and the maximally Abelian gauge (MAG) [130,[386][387][388]. Such analyses were made possible by the combination of the functional RG and DSEs as initially introduced in [383] or under the assumption of a convergent skeleton expansion [307,384].…”

Section: Two-loop Diagrams In the Gluon Propagator Dsementioning

confidence: 99%

“…Since the MAG can be introduced in the same way as the Landau gauge by minimizing a Lorentz invariant gauge fixing functional, it is not only also directly accessible for lattice calculations [514][515][516][517][518][519], but also the Gribov-Zwanziger construction of an improved gauge fixing can be done in a similar way [249,251,253,520]. Finally, also functional methods were used to investigate the correlation functions of the MAG [130,388,390,521]. With functional equations, the focus was on the study of the scaling solution.…”

Section: Abelian Dominance In the Correlation Functions Of The Maxima...mentioning

confidence: 99%

Nonperturbative properties of Yang-Mills theories

Huber¹

2018

Preprint

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Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations. They also provide access to the phase diagram. Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson-Schwinger equations. Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang-Mills theories.

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Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance

Cited by 4 publications

References 25 publications

Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

Yang-Mills propagators in linear covariant gauges from Nielsen identities

Nonperturbative properties of Yang-Mills theories

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