Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory

TL;DR

This paper investigates the infrared behavior of vertex functions in Landau gauge SU(N) Yang-Mills theory, revealing singularities, an infrared fixed point for the running coupling, and the dominance of ghost-loop diagrams in the infrared.

Contribution

It provides a detailed analysis of the infrared structure of vertex functions using Dyson-Schwinger equations, highlighting the conditions for singularities and the fixed point behavior.

Findings

Three- and four-gluon vertices become singular at zero external momenta.

The running coupling exhibits an infrared fixed point.

Ghost-loop diagrams dominate in the infrared regime.

Abstract

The infrared behaviour of vertex functions in an SU(N) Yang-Mills theory in Landau gauge is investigated employing a skeleton expansion of the Dyson-Schwinger equations. The three- and four-gluon vertices become singular if and only if all external momenta vanish while the dressing of the ghost-gluon vertex remains finite in this limit. The running coupling as extracted from either of these vertex functions possesses an infrared fixed point. In general, diagrams including ghost-loops dominate in the infrared over purely gluonic ones.