Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II

TL;DR

This paper simplifies and extends a proof of the unique infrared scaling solution in Landau gauge Yang-Mills theory, using a new RG-invariant approach that applies broadly and confirms the existence of a specific consistent scaling solution.

Contribution

The paper introduces a simplified, RG-invariant method to prove the uniqueness of the infrared scaling solution in Landau gauge Yang-Mills theory, applicable to general theories.

Findings

Confirmed the existence of a specific scaling solution for DSEs and FRGs.

Demonstrated the solution exhibits uniform and soft kinematic singularities.

Provided a more accessible proof of the uniqueness of the infrared asymptotics.

Abstract

We present a shortened and simplified version of our proof \cite{Fischer:2006vf} of the uniqueness of the scaling solution for the infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. The simplification relates to a new RG-invariant arrangement of Green functions applicable to general theories. As before the proof relies on the necessary consistency between Dyson-Schwinger equations (DSEs) and functional renormalisation group equations (FRGs). We also demonstrate the existence of a specific scaling solution for both, DSEs and FRGs, that displays uniform and soft kinematic singularities.