On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge

TL;DR

This paper introduces an improved method for analyzing infrared behavior in SU(N) Yang-Mills theories within the maximally Abelian gauge, confirming the Abelian dominance hypothesis through scaling solutions.

Contribution

It generalizes the analysis of infrared exponents to complex systems like Yang-Mills theory in the maximally Abelian gauge, providing a systematic approach and explicit solutions.

Findings

Infrared enhanced diagonal gluon propagator supports Abelian dominance.

Scaling solutions are explicitly derived for SU(2) and SU(N).

Conditions for the existence of infrared scaling solutions are established.

Abstract

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators' infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost anti-ghost symmetric gauges.