Decomposition of SU(N) connection and effective theory of SU(N) QCD

We give a general decomposition of SU(N) connection and derive a generalized Skyrme–Faddeev action as the effective action of SU(N) QCD in the low energy limit. The result is obtained by separating the topological degrees which describes the non-Abelian monopoles from the dynamical degree of gauge potential, and integrating all the dynamical degrees of SU(N) QCD.