A non-perturbative study of the correlation functions of three-dimensional Yang-Mills theory

TL;DR

This paper presents a non-perturbative analysis of three-dimensional Yang-Mills theory using equations of motion, capturing the behavior of correlation functions and vertices with a comprehensive truncation scheme.

Contribution

It introduces a self-contained truncation including propagators and vertices, incorporating two-loop diagrams and exploring divergence subtraction methods.

Findings

Gluon propagator deviations are significant only at low momenta.

Vertex-derived couplings agree well down to a few GeV.

Higher gluonic correlations show sizable deviations from tree-level at low momenta.

Abstract

Yang-Mills theory is studied in three dimensions using the equations of motion of the $1$PI and $3$PI effective actions. The employed self-contained truncation includes the propagators, the three-point functions and the four-gluon vertex dynamically. In the gluon propagator also two-loop diagrams are taken into account. The higher gluonic correlation functions show sizable deviations from the tree-level only at low momenta. Also the couplings derived from the vertices agree well down to a few GeV. In addition, different methods to subtract spurious divergences are explored.