New Faddeev–Niemi-type variables for the static Yang–Mills theory

Faddeev and Niemi introduced a nonlinear sigma model as a natural extension of the Faddeev $SU(2)$ chiral model. The field variables in the extended model are two chiral fields taking values in $SU(3)/(U(1)\times U(1))$ and $SU(3)/(SU(2)\times U(1))$. Shabanov showed that the energy functional of the extended model is bounded from below by a topological invariant and can therefore support knotlike excitations and a mass gap. We introduce new variables of the Faddeev–Niemi type for the static $SU(3)$ Yang–Mills theory, which reveal a structure of a nonlinear sigma model in the Lagrangian.