Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations

TL;DR

This paper computes the two- and three-point functions and the four-gluon vertex in three-dimensional Yang-Mills theory using Dyson-Schwinger equations, analyzing truncation effects and comparing with lattice results.

Contribution

It provides a detailed study of truncation effects in Dyson-Schwinger equations for 3D Yang-Mills theory and estimates errors from various approximations.

Findings

Two-loop diagrams are crucial for the gluon propagator.

Four-gluon vertex has a small impact on lower Green functions.

Truncation effects can be estimated through comparisons and error analysis.

Abstract

The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the 3PI effective action. Within a self-contained truncation various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results, and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.