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.
@article{arxiv.hep-th/9611074,
title = {Is N=4 Yang-Mills Theory Soluble?},
author = {P. S. Howe and P. C. West},
journal= {arXiv preprint arXiv:hep-th/9611074},
year = {2007}
}