Partial duality in SU(N) Yang-Mills theory

Recently we have proposed a set of variables for describing the infrared limit of four dimensional SU(2) Yang-Mills theory. Here we extend these variables to the general case of four dimensional SU(N) Yang-Mills theory. We find that the SU(N) connection Aμ decomposes according to irreducible representations of SO(N−1), and the curvature two form Fμν is related to the symplectic Kirillov two forms that characterize irreducible representations of SU(N). We propose a general class of nonlinear chiral models that may describe stable, soliton-like configurations with nontrivial topological numbers.