Yang-Mills theory constructed from Cho--Faddeev--Niemi decomposition

TL;DR

This paper reinterprets the Cho--Faddeev--Niemi decomposition of Yang-Mills theory, clarifying gauge symmetry restrictions and providing new insights into gauge invariance, observables, and connections to the Skyrme--Faddeev model.

Contribution

It introduces a novel perspective on the CFN decomposition, explaining how to restrict gauge symmetry to recover the original Yang-Mills theory with its symmetries.

Findings

Clarifies the gauge symmetry restriction in CFN decomposition.

Provides new understanding of gauge invariance and observables.

Discusses implications for the Skyrme--Faddeev model.

Abstract

We give a new way of looking at the Cho--Faddeev--Niemi (CFN) decomposition of the Yang-Mills theory to answer how the enlarged local gauge symmetry respected by the CFN variables is restricted to obtain another Yang-Mills theory with the same local and global gauge symmetries as the original Yang-Mills theory. This may shed new light on the fundamental issue of the discrepancy between two theories for independent degrees of freedom and the role of the Maximal Abelian gauge in Yang-Mills theory. As a byproduct, this consideration gives new insight into the meaning of the gauge invariance and the observables, e.g., a gauge-invariant mass term and vacuum condensates of mass dimension two. We point out the implications for the Skyrme--Faddeev model.