Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

Maas, Axel; Pawlowski, Jan M.; Spielmann, Daniel; Sternbeck, André; Smekal, Lorenz von

doi:10.1140/epjc/s10052-010-1306-6

Cited by 48 publications

(64 citation statements)

References 88 publications

(172 reference statements)

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“…Secondly, almost all lattice calculations of the gluon propagator favor a decoupling solution. But lattice studies at strong coupling [27][28][29] reveal the existence of a regime where the scaling relation between the gluon and the ghost propagator is fulfilled, and the corresponding infrared exponent κ is very close to the value determined in truncated continuum studies with κ = 0.595. A potential resolution of this puzzle has been offered recently in Ref.…”

Section: Infrared Structure Of Landau Gauge Yang-mills Theorysupporting

confidence: 55%

QCD Green's Functions and Phases of Strongly-Interacting Matter

Alkofer

Mitter

Schaefer

2011

EPJ Web of Conferences

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Abstract. After presenting a brief summary of functional approaches to QCD at vanishing temperatures and densities the application of QCD Green's functions at non-vanishing temperature and vanishing density is discussed. It is pointed out in which way the infrared behavior of the gluon propagator reflects the (de-)confinement transition. Numerical results for the quark propagator are given thereby verifying the relation between (de-)-confinement and dynamical chiral symmetry breaking (restoration). Last but not least some results of DysonSchwinger equations for the color-superconducting phase at large densities are shown.

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Section: Infrared Structure Of Landau Gauge Yang-mills Theorysupporting

confidence: 55%

QCD Green's Functions and Phases of Strongly-Interacting Matter

Alkofer

Mitter

Schaefer

2011

EPJ Web of Conferences

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“…This is certainly true if one takes into account only the available data for the gluon propagator in the usual minimal Landau gauge. On the other hand, going to the extreme strong-coupling limit not only the infared exponents of the decoupling but also the exponents of the scaling solution can be extracted [17,18,19]. To my opinion such an extraction should be absolutely impossible if the scaling solution is definitely absent and therefore the lattice calculations should not contain any trace of it.…”

Section: A Comment On the Infrared Behaviour Of Landau Gauge Green Fumentioning

confidence: 96%

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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“…The bottom panels show the same, but for gauge algebras su(3-6) and g 2 in MLG [175]. Further lattice results can be found in [91,95,117,118,122,135,253] The situation for the maxB gauge is drastically different [84]. In this case, the ghost propagator is much more divergent than even the scaling case, and more divergent than the results in any of the other gauges.…”

Section: Correlation Functions 411 Propagatorsmentioning

confidence: 97%

“…The bottom panels show the same, but for gauge algebras su(3-6) and g 2 in MLG [175]. Further lattice results can be found in [91,95,117,118,123,135,251,[253][254][255].…”

Section: Correlation Functions 411 Propagatorsmentioning

confidence: 99%

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Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

Cited by 48 publications

References 88 publications

QCD Green's Functions and Phases of Strongly-Interacting Matter

QCD Green's Functions and Phases of Strongly-Interacting Matter

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

Gauge bosons at zero and finite temperature

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