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 nonperturbative 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 nonvanishing 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 $\ensuremath{\beta}=4.2$ and $\ensuremath{\beta}=6.0$. 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.