SU(4) harmonic superspace and supersymmetric gauge theory
  We consider the harmonic-superspace formalism in the $N=4$ supersymmetry using the $SU(4)/SU(2)\times SU(2)\times U(1)$ harmonics which was earlier applied to the abelian gauge theory. The N=4 non-abelian constraints in a standard superspace are reformulated as the harmonic-superspace equations for two basic analytic superfields: the independent superfield strength W of a dimension 1 and the dimensionless harmonic gauge 4-prepotential V having the $U(1)$ charge 2. These constraint equations I manifestly depend on the Grassmann coordinates $\theta$, although they are covariant under the unusual N=4 supersymmetry transformations. We analyze an alternative harmonic formalism of the supergauge theory for two unconstrained nonabelian analytic superfields W and V. The gauge-invariant action A(W,V) in this formalism contains $\theta$ factors in each term, it is invariant under the $SU(4)$ automorphism group. In this model, the interaction of two infinite-dimensional N=4 supermultiplets with the physical and auxiliary fields arises at the level of component fields. The action A(W,V) generate analytic equations of motion II alternative to the harmonic-superspace superfield constraints I. Both sets of equations give us the equivalent equations for the physical component fields of the $N=4$ gauge supermultiplet, they connect auxiliary and physical fields of two superfields. The nonlinear effective interaction of the abelian harmonic superfield W is constructed. 
B.M. Zupnik
hep-th