QCD versus Skyrme-Faddeev Theory

TL;DR

This paper explores how the Cho decomposition modifies QCD dynamics, reveals topological similarities with the Skyrme-Faddeev theory, and suggests both theories describe confinement via monopole flux.

Contribution

It demonstrates that the Cho decomposition makes the topological degrees of QCD dynamical and links QCD with the Skyrme-Faddeev theory through monopole structures.

Findings

Cho decomposition enlarges QCD's dynamical degrees.

Skyrme-Faddeev theory shares topological structures with QCD.

Faddeev-Niemi knots relate to QCD vacua.

Abstract

We discuss the physical impacts of the ``Cho decomposition'' (or the ``Cho-Faddeev-Niemi-Shabanov decomposition'') of the non-Abelian gauge potential on QCD. We show how the decomposition makes a subtle but important modification on the non-Abelian dynamics, and present three physically equivalent quantization schemes of QCD which are consistent with the decomposition. In particular, we show that the decomposition enlarges the dynamical degrees of QCD by making the topological degrees of the non-Abelian gauge symmetry dynamical. Furthermore with the decomposition we show that the Skyrme-Faddeev theory of non-linear sigma model and QCD have almost identical topological structures. In specific we show that an essential ingredient in both theories is the Wu-Yang type non-Abelian monopole, and that the Faddeev-Niemi knots of the Skyrme-Faddeev theory can actually be interpreted to describe the multiple vacua of the SU(2) QCD. Finally we argue that the Skyrme-Faddeev theory is, just like QCD, a theory of confinement which confines the magnetic flux of the monopoles.