Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory

TL;DR

This paper generalizes the Faddeev-Niemi decomposition for SU(3) Yang-Mills theory, providing an off-shell complete decomposition for SU(3) -> U(2) and exploring topological implications related to gauge symmetry breaking.

Contribution

It introduces a generalized decomposition for SU(N+1) -> U(N) and achieves an off-shell complete decomposition for SU(3) -> U(2), extending the original FN framework.

Findings

Off-shell complete decomposition for SU(3) -> U(2)

No FN knot solitons for nonabelian unbroken symmetry

Reaffirmation of no-go theorems for colored dyons

Abstract

Faddeev and Niemi (FN) have introduced an abelian gauge theory which simulates dynamical abelianization in Yang-Mills theory (YM). It contains both YM instantons and Wu-Yang monopoles and appears to be able to describe the confining phase. Motivated by the meson degeneracy problem in dynamical abelianization models, in this note we present a generalization of the FN theory. We first generalize the Cho connection to dynamical symmetry breaking pattern SU(N+1) -> U(N), and subsequently try to complete the Faddeev-Niemi decomposition by keeping the missing degrees of freedom. While it is not possible to write an on-shell complete FN decomposition, in the case of SU(3) theory of physical interest we find an off-shell complete decomposition for SU(3) -> U(2) which amounts to partial gauge fixing, generalizing naturally the result found by Faddeev and Niemi for the abelian scenario SU(N+1) -> U(1)^N. We discuss general topological aspects of these breakings, demonstrating for example that the FN knot solitons never exist when the unbroken gauge symmetry is nonabelian, and recovering the usual no-go theorems for colored dyons.