Infrared saturation and phases of gauge theories with BRST symmetry

Mader, Valentin; Schaden, Martin; Zwanziger, Daniel; Alkofer, Reinhard

doi:10.1140/epjc/s10052-014-2881-8

Cited by 26 publications

(27 citation statements)

References 122 publications

(186 reference statements)

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“…An approach that strengthens the evidence for confinement being related to the behaviour of Green's function in the extreme infrared only is based on the study of the gluon's quantum equation of motion and how its saturation in the infrared by physical or unphysical degrees of freedom distinguishes between the Coulomb, the Higgs and the confining phase of a gauge theory [148]. This investigation also further elucidates the role of the BRST symmetry of the gaugefixed theory for several types of confinement scenarios, see also the reviews [149,150] and references therein.…”

Section: Confinementmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

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438

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: Confinementmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

Self Cite

438

530

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“…There are also studies from a perspective of the KugoOjima (KO) criterion and the Gribov problem. The KO criterion has been generalized to the MA gauge in a very recent paper [16] and there are also the Gribov copies in the MA gauge, located on the other side of the horizon [22][23][24]. The gluon propagator in the MA gauge has been also studied on the basis of the original Gribov's work and the horizon term in the MA gauge, corresponding to that in the Landau gauge has been studied [2,3,22].…”

Section: Introductionmentioning

confidence: 99%

Gribov-Zwanziger action in SU(2) maximally Abelian gauge withU(1)3Landau gauge

Gongyo

Iida

2014

Phys. Rev. D

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We construct the local Gribov-Zwanziger action for SU(2) Euclidean Yang-Mills theories in the maximally Abelian (MA) gauge with U(1)3 Landau gauge fixing based on the Zwanziger's work in the Landau gauge. By the restriction of the functional integral region to the Gribov region in the MA gauge, we give the nonlocal action. We localize the action with new fields and obtain the action with the shift of the new scalar fields, which has the terms, corresponding to the localized action of the horizon function in the MA gauge. The diagonal gluon propagator in the MA gauge at tree level behaves like the propagator from Gribov-Zwanziger action in the Landau gauge and shows the violation of Kallen-Lehmann representation.

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“…They may then be expressed in terms of the shifted variables. and the generator of rigid color rotations, Q C , of the GZ-theory is [9,14], …”

Section: Resultsmentioning

confidence: 99%

“…We here extend, and review for completeness, the analysis in [9] of the Kugo-Ojima confinement criterion [6,7] and the GZ action.…”

Section: Tree-level Evaluation Of the Trace Anomalymentioning

confidence: 90%

“…This is promising for the confinement problem, because the Kugo-Ojima criterion is a sufficient condition for color confinement, and the horizon condition assures that this condition is satisfied in the GZ approach. Although the identity of these two conditions has been noted for some time [8,9], its consequences have remained obscure because the Kugo-Ojima confinement criterion requires BRST symmetry [10] to be unbroken, whereas the GZ vacuum breaks BRST symmetry. This breaking is manifested by the non-zero vacuum expectation value of a BRST-exact quantity such as vac|{Q B ,ω}|vac = 0, (1.2) whereω is an auxiliary ghost field of GZ theory, Q B is the BRST charge, and |vac is the vacuum state.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Living with spontaneously broken BRST symmetry. I. Physical states and cohomology

Schaden

Zwanziger

2015

Phys. Rev. D

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Abstract:We address the issue of Becchi-Rouet-Stora-Tyutin (BRST) symmetry breaking in the Gribov-Zwanziger (GZ) model, a local, renormalizable, nonperturbative approach to QCD. Explicit calculation of several examples reveals that BRST symmetry breaking apparently afflicts the unphysical sector of the theory, but may be unbroken where needed, in cases of physical interest. Specifically, the BRSTexact part of the conserved energy-momentum tensor and the BRST-exact term in the Kugo-Ojima confinement condition both have vanishing expectation value. We analyze the origin of the breaking of BRST symmetry in the GZ model, and obtain a useful sufficient condition that determines which operators preserve BRST.Observables of the GZ theory are required to be invariant under a certain group of symmetries that includes not only BRST but also others. The definition of observables is thereby sharpened, and excludes all operators known to us that break BRST invariance. We take as a hypothesis that BRST symmetry is unbroken by this class of observables. If the hypothesis holds, BRST breaking is relegated to the unphysical sector of the GZ theory, and its physical states are obtained by the usual cohomological BRST construction. The fact that the horizon condition and the Kugo-Ojima confinement criterion coincide assures that color is confined in the GZ theory.

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Infrared saturation and phases of gauge theories with BRST symmetry

Cited by 26 publications

References 122 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Gribov-Zwanziger action in SU(2) maximally Abelian gauge withU(1)3Landau gauge

Living with spontaneously broken BRST symmetry. I. Physical states and cohomology

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