Infrared Non-perturbative Propagators of Gluon and Ghost via Exact Renormalization Group

TL;DR

This paper uses the exact renormalization group to analyze infrared behavior of gluon and ghost propagators in Yang-Mills theory, revealing that including momentum-dependent four-point vertices is crucial for consistent solutions.

Contribution

It introduces a non-perturbative ERG approach that incorporates four-point vertices with momentum dependence, providing a new perspective on infrared propagator behavior.

Findings

Infrared power law behavior of propagators obtained as an attractive solution.

Including momentum-dependent four-point vertices prevents RG flow divergence.

ERG results are compared with Schwinger-Dyson equation analyses.

Abstract

The recent investigations of pure Landau gauge SU(3) Yang-Mills theories which are based on the truncated Schwinger-Dyson equations (SDE) indicate an infrared power law behavior of the gluon and the ghost propagators. It has been shown that the gluon propagator vanishes (or finite) in the infrared limit, while the ghost propagator is more singular than a massless pole, and also that there exists an infrared fixed point of the running gauge coupling. In this paper we reexamine this picture by means of the exact (non-perturbative) renormalization group (ERG) equations under some approximation scheme, in which we treat not only two point functions but also four point vertices in the effective average action with retaining their momentum dependence. Then it is shown that the gluon and the ghost propagators with the infrared power law behavior are obtained as an attractive solution starting from rather arbitrary ultraviolet bare actions. Here it is found to be crucial to include the momentum dependent four point vertices in the ERG framework, since otherwise the RG flows diverge at finite scales. The features of the ERG analyses in comparison with the SDE are also discussed.