Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition

TL;DR

This paper computes the Wilsonian effective action for SU(2) Yang-Mills theory using the Cho-Faddeev-Niemi-Shabanov decomposition, revealing mass scale generation and the importance of higher-derivative terms for topological solitons.

Contribution

It introduces a one-loop calculation of the effective action employing this decomposition, highlighting the role of higher-derivative terms in describing knotlike solitons.

Findings

Mass scale is generated in the effective action.

Higher-derivative terms are necessary for topological solitons.

Flow of marginal couplings is analyzed.

Abstract

The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the flow of the marginal couplings is studied. Our results indicate that higher-derivative terms of the color-unit-vector $\mathbf{n}$ field are necessary for the description of topologically stable knotlike solitons which have been conjectured to be the large-distance degrees of freedom.