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

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.

18 pages, 12 figures, 3 tables

References in corpus (3)

• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD

Cited by in corpus (17)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Three-point vertices in Landau-gauge Yang-Mills theory
• Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory
• Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• The infrared behavior of Landau gauge Yang-Mills theory in d=2, 3 and 4 dimensions
• Just how different are SU(2) and SU(3) Landau-gauge propagators in the IR regime?
• The running coupling from the four-gluon vertex in Landau gauge Yang-Mills theory
• A first look at Landau-gauge propagators in G2 Yang-Mills theory
• Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge
• Linear Covariant Gauges on the Lattice
• Instantons, monopoles, vortices, and the Faddeev-Popov operator eigenspectrum
• Green's Functions and Topological Configurations
• A Numerical Approach to Coulomb Gauge QCD
• Lower dimensional Yang-Mills theory as a laboratory to study the infrared regime