Faddeev–Niemi conjecture and effective action of QCD

We calculate a one loop effective action of SU(2) QCD in the presence of the monopole background, and find a possible connection between the resulting QCD effective action and a generalized Skyrme–Faddeev action of the non-linear sigma model. The result is obtained using the gauge-independent decomposition of the gauge potential into the topological degrees which describes the non-Abelian monopoles and the local dynamical degrees of the potential, and integrating out all the dynamical degrees of QCD.