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Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory

Attilio Cucchieri·Axel Maas·Tereza Mendes
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Abstract

Green's functions are a central element in the attempt to understand non-perturbative phenomena in Yang-Mills theory. Besides the propagators, 3-point Green's functions play a significant role, since they permit access to the running coupling constant and are an important input in functional methods. Here we present numerical results for the two non-vanishing 3-point Green's functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e. the three-gluon vertex and the ghost-gluon vertex, considering various kinematical regimes. In this exploratory investigation the lattice volumes are limited to 20^3 and 30^3 at beta=4.2 and beta=6.0. We also present results for the gluon and the ghost propagators, as well as for the eigenvalue spectrum of the Faddeev-Popov operator. Finally, we compare two different numerical methods for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source and the plane-wave-source methods.

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Attilio Cucchieri, Axel Maas, Tereza Mendes. 2006-05-14. Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory. https://doi.org/10.1103/physrevd.74.014503

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