Spectral dimension as a tool for analyzing nonperturbative propagators

Kern, Wolfgang; Huber, Markus Q.; Alkofer, Reinhard

doi:10.1103/physrevd.100.094037

Cited by 13 publications

(8 citation statements)

References 84 publications

(135 reference statements)

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“…The appearance of this maximum is inextricably connected with the presence of the unprotected logarithm originating from the ghost loop. In addition to confirming the known nonperturbative behavior of the ghost propagator in Euclidean space (i.e., absence of a "ghost mass"), it has a direct implication on the general analytic structure of the gluon propagator [48,93]. In particular, from the standard Källén-Lehmann representation [94,95]…”

Section: A Basic Concepts and Key Relationsmentioning

confidence: 80%

Gluon propagator and three-gluon vertex with dynamical quarks

et al. 2020

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We present a detailed analysis of the kinetic and mass terms associated with the Landau gauge gluon propagator in the presence of dynamical quarks, and a comprehensive dynamical study of certain special kinematic limits of the three-gluon vertex. Our approach capitalizes on results from recent lattice simulations with (2+1) domain wall fermions, a novel nonlinear treatment of the gluon mass equation, and the nonperturbative reconstruction of the longitudinal three-gluon vertex from its fundamental Slavnov-Taylor identities. Particular emphasis is placed on the persistence of the suppression displayed by certain combinations of the vertex form factors at intermediate and low momenta, already known from numerous pure Yang-Mills studies. One of our central findings is that the inclusion of dynamical quarks moderates the intensity of this phenomenon only mildly, leaving the asymptotic low-momentum behavior unaltered, but displaces the characteristic "zero crossing" deeper into the infrared region. In addition, the effect of the three-gluon vertex is explored at the level of the renormalization-group invariant combination corresponding to the effective gauge coupling, whose size is considerably reduced with respect to its counterpart obtained from the ghost-gluon vertex. The main upshot of the above considerations is the further confirmation of the tightly interwoven dynamics between the two-and three-point sectors of QCD.

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Section: A Basic Concepts and Key Relationsmentioning

confidence: 80%

Gluon propagator and three-gluon vertex with dynamical quarks

et al. 2020

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“…In particular, the gluon propagator has a shallow/pronounced maximum from which it follows immediately that it violates positivity. Note that such a property also leads to a spectral dimension of one in the deep IR [83]. Correspondingly, if the maximum vanished, this would imply a qualitative change of the type of solution, and it is reassuring that we do not observe that.…”

Section: Resultsmentioning

confidence: 73%

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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“…This also explains why the maximum in the gluon propagator is difficult to observe in lattice results for four dimensions [64,67,69]. In general, however, there are additional arguments for the existence of a maximum from both continuum analyses, e.g., [99,113] and from three-dimensional lattice calculations, e.g., [96,114,115]. The observed maximum in the gluon propagator directly leads to a violation of positivity of the spectral function, see, e.g., [94,99,116,117].…”

Section: A Propagatorsmentioning

confidence: 97%

“…For the Higgs-type solutions, the maximum is at zero. The existence of a maximum at nonvanishing momenta does not only lead to positivity violation of the propagator [15], it also reduces the spectral dimension, viz., the dimension felt by the propagator [99], from four to one. The calculations in this work span solutions from scaling to the boundary of the Higgs-branch.…”

Section: Renormalizationmentioning

confidence: 99%

“…In general, however, there are additional arguments for the existence of a maximum from both continuum analyses, e.g., [99,113] and from three-dimensional lattice calculations, e.g., [96,114,115]. The observed maximum in the gluon propagator directly leads to a violation of positivity of the spectral function, see, e.g., [94,99,116,117]. This is reflected in the Schwinger function calculated from the propagator as…”

Section: A Propagatorsmentioning

confidence: 99%

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Correlation functions of Landau gauge Yang-Mills theory

Huber

2020

Preprint

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Correlation functions of Yang-Mills theory in the Landau gauge are calculated from their equations of motion. The employed setup is completely parameter-free and leads, within errors, to good quantitative agreement with corresponding lattice results for the ghost and gluon propagators as well as the ghost-gluon and three-gluon vertices. Also the four-gluon vertex is calculated. The present setup allows for the first time for a unique subtraction of quadratic divergences in the gluon propagator Dyson-Schwinger equation. Thus, there are no ambiguities which can arise due to the use of models or auxiliary workarounds. In addition, several self-tests of the results are described that allow assessing the truncation error in a self-consistent way. This enables a new perspective on how to identify limitations of the present setup and develop future improvements.

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Spectral dimension as a tool for analyzing nonperturbative propagators

Cited by 13 publications

References 84 publications

Gluon propagator and three-gluon vertex with dynamical quarks

Gluon propagator and three-gluon vertex with dynamical quarks

Yang-Mills propagators in linear covariant gauges from Nielsen identities

Correlation functions of Landau gauge Yang-Mills theory

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