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The anti-de Sitter/conformal field theory duality conjecture raises thequestion of how the perturbative expansion in the conformal field theory canresum to a simple function. We exhibit a relation between the one-loop andtwo-loop amplitudes whose generalization to higher-point and higher-loopamplitudes would answer this question. We also provide evidence for the firstof these generalizations.Comment: 6 pages, talk given at the 3rd International Symposium on Quantum  Theory and Symmetries, Cincinnati, OH, Sept 10-14, 2003; v2: Mispositioned  figure in eqn. 1 fixe

CROSS-ORDER RELATIONS IN ${\mathcal N} = 4$ SUPERSYMMETRIC GAUGE THEORIES