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 supersymm etric Yang-Mills theory are studied using N = 2 harmonic superspace perturb ation theory The results are expressed in terms of differential operators a cting on a scalar two-loop integral. The leading singular behaviour is obta ined in the limit that two of the points approach one another. We find loga rithmic singularities which do not cancel out in the sum of all diagrams. I t is confirmed that Green's functions of analytic operators are indeed anal ytic at this order in perturbation theory. (C) 1999 Elsevier Science B.V. A ll rights reserved.