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Title: Landau gauge Yang-Mills correlation functions

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 94; Journal Issue: 5; Related Information: CHORUS Timestamp: 2016-09-06 18:09:26; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Cyrol, Anton K., Fister, Leonard, Mitter, Mario, Pawlowski, Jan M., and Strodthoff, Nils. Landau gauge Yang-Mills correlation functions. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.94.054005.
Cyrol, Anton K., Fister, Leonard, Mitter, Mario, Pawlowski, Jan M., & Strodthoff, Nils. Landau gauge Yang-Mills correlation functions. United States. doi:10.1103/PhysRevD.94.054005.
Cyrol, Anton K., Fister, Leonard, Mitter, Mario, Pawlowski, Jan M., and Strodthoff, Nils. 2016. "Landau gauge Yang-Mills correlation functions". United States. doi:10.1103/PhysRevD.94.054005.
title = {Landau gauge Yang-Mills correlation functions},
author = {Cyrol, Anton K. and Fister, Leonard and Mitter, Mario and Pawlowski, Jan M. and Strodthoff, Nils},
abstractNote = {},
doi = {10.1103/PhysRevD.94.054005},
journal = {Physical Review D},
number = 5,
volume = 94,
place = {United States},
year = 2016,
month = 9

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevD.94.054005

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Cited by: 6works
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  • We analyze the complete algebraic structure of the background field method for Yang-Mills theory in the Landau gauge and show several structural simplifications within this approach. In particular, we present a new way to study the IR behavior of Green functions in the Landau gauge and show that there exists a unique Green function whose IR behavior controls the IR properties of the gluon and the ghost propagators.
  • The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in three and four dimensions. The propagators and the Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario. In addition, finite-volume effects affecting these Green's functions are investigated systematically. The critical infrared exponents of the propagators, as proposed in calculations using stochastic quantization and Dyson-Schwinger equations, are confirmed quantitatively. For this purpose lattices of volume up to (42.7 fm){sup 2} have beenmore » used.« less
  • Massive renormalizable Yang-Mills theories in three dimensions are analyzed within the algebraic renormalization in the Landau gauge. In analogy with the four-dimensional case, the renormalization of the mass operator A{mu}aA{mu}a turns out to be expressed in terms of the fields and coupling constant renormalization factors. We verify the relation we obtain for the operator anomalous dimension by explicit calculations in the large N{sub f} expansion. The generalization to other gauges such as the non-linear Curci-Ferrari gauge is briefly outlined.
  • The local composite operator A{sub {mu}}{sup 2} is added to the Zwanziger action, which implements the restriction to the Gribov region {omega} in Euclidean Yang-Mills theories in the Landau gauge. We prove that Zwanziger's action with the inclusion of the operator A{sub {mu}}{sup 2} is renormalizable to all orders of perturbation theory, obeying the renormalization group equations. This allows us to study the dimension two gluon condensate <A{sub {mu}}{sup 2}> by the local composite operator formalism when the restriction to the Gribov region {omega} is taken into account. The resulting effective action is evaluated at one-loop order in the MSmore » scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to <A{sub {mu}}{sup 2}>, but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without the inclusion of the condensate <A{sub {mu}}{sup 2}>, are investigated. In particular, it is shown that in the original Gribov-Zwanziger formulation, i.e. without the inclusion of the operator A{sub {mu}}{sup 2}, the resulting vacuum energy is always positive at one-loop order, independently from the choice of the renormalization scheme and scale. In the presence of <A{sub {mu}}{sup 2}>, we are unable to come to a definite conclusion at the order considered. In the MS scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. Concerning the behavior of the gluon and ghost propagators, we recover the well-known consequences of the restriction to the Gribov region, and this in the presence of <A{sub {mu}}{sup 2}>, i.e. an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. Such a behavior is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.« less
  • A semiperturbative calculation of the ghost-gluon vertex in Landau-gauge Yang-Mills theory in four and three Euclidean space-time dimensions is presented. Nonperturbative gluon and ghost propagators are employed, which have previously been calculated from a truncated set of Dyson-Schwinger equations and which are in qualitative and quantitative agreement with corresponding lattice results. Our results for the ghost-gluon vertex show only relatively small deviations from the tree-level one in agreement with recent lattice data. In particular, we do not see any sign for a singular behavior of the ghost-gluon vertex in the infrared.