Is N=4 Yang-Mills Theory Soluble?

The superconformal properties of N=4 Yang-Mills theory are most naturally studied using the formalism of harmonic superspace. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces and it is argued that the theory is soluble for a class of such operators.