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

TL;DR

This study explores three-point Green's functions in 3d SU(2) Yang-Mills theory using lattice simulations, providing insights into non-perturbative phenomena and comparing numerical methods for Faddeev-Popov matrix inversion.

Contribution

It presents the first numerical results for specific three-point Green's functions in 3d Landau-gauge Yang-Mills theory, including a comparison of computational techniques.

Findings

Measured three-gluon and ghost-gluon vertices across kinematic regimes.

Analyzed gluon and ghost propagators and Faddeev-Popov spectrum.

Compared point-source and plane-wave-source methods for matrix inversion.

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.