SU(4) harmonic superspace and supersymmetric gauge theory

We consider the harmonic superspace formalism in N=4 supersymmetry based on SU(4)/SU(2)×SU(2)×U(1) harmonics, which was previously used in Abelian gauge theory. We propose a transformation of non-Abelian constraints in the standard N=4 superspace into a superfield equation for two basic analytic superfields: an independent strength W of dimension one and a dimensionless harmonic four-prepotential V of the U(1) charge two. These constraint equations I explicitly depend on the Grassmann coordinates ѳ, although they are covariant under nonstandard N=4 supersymmetry transformations. The component expansion of superfield equations I generates the known equations for physical fields of the N=4 supermultiplet, with the auxiliary fields vanishing or expressible in terms of physical fields on the mass shell. In the harmonic formalism of N=4 supergauge theory off the mass shell, we construct a gauge-invariant action A(W, V) for two unconstrained non-Abelian analytic superfields W and V; this action contains theta factors in each term and is invariant under the SU(4) automorphism group and scaling transformations. At the level of component fields, this model acquires an interaction of two infinite-dimensional N=4 supermultiplets involving physical and auxiliary fields. The action A(W, V) generates analytic equations of motion II, alternative to the superfield constraints I. Both sets of equations give equivalent equations for physical component fields of the N=4 gauge supermultiplet. We construct a nonlinear effective interaction for the Abelian harmonic superfield W.