Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge

TL;DR

This paper investigates the infrared behavior of propagators and vertices in Yang--Mills theory within Landau and Coulomb gauges, revealing gauge-dependent exponents and the robustness of ghost-gluon vertex dressing.

Contribution

It provides a detailed analysis of the infrared exponents and vertex behaviors in different gauges, including analytical and numerical results, under the assumption of ghost dominance.

Findings

Unique infrared exponent in 4D Landau gauge

Two different infrared exponents in Coulomb gauge

Ghost-gluon vertex dressing does not affect infrared exponents

Abstract

The infrared behaviour of gluon and ghost propagators, ghost-gluon vertex and three-gluon vertex is investigated for both the covariant Landau and the non-covariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behaviour of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the Coulomb gauge.