Four - point functions in N = 4 supersymmetric Yang - Mills theory at two loops

Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetric Yang-Mills theory are studied using N = 2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities which do not cancel out in the sum of all diagrams. It is confirmed that Green's functions of analytic operators are indeed analytic at this order in perturbation theory.