The infrared fixed point of Landau gauge Yang-Mills theory: A renormalization group analysis

TL;DR

This paper uses renormalization group equations to analyze the infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theory, showing decoupling solutions as infrared-stable in dimensions >2, aligning with lattice results.

Contribution

It demonstrates how Callan-Symanzik renormalization group equations reproduce both scaling and decoupling solutions, identifying decoupling as the infrared-stable solution for higher dimensions.

Findings

Decoupling solutions are infrared-stable for dimensions greater than two.

The renormalization group approach reproduces known solutions of Dyson-Schwinger equations.

Results align with recent lattice calculations.

Abstract

The infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theory has been at the center of an intense debate over the last decade. Different solutions of the Dyson-Schwinger equations show a different behavior of the propagators in the infrared: in the so-called scaling solutions both propagators follow a power law, while in the decoupling solutions the gluon propagator shows a massive behavior. The latest lattice results favor the decoupling solutions. In this contribution, after giving a brief overview of the present status of analytical and semi-analytical approaches to the infrared regime of Landau gauge Yang-Mills theory, we will show how Callan-Symanzik renormalization group equations in an epsilon expansion reproduce both types of solutions and single out the decoupling solutions as the infrared-stable ones for space-time dimensions greater than two, in agreement with the lattice calculations.