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We study the subleading-color (nonplanar) contributions to the four-gluonscattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory. Using theformalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicitexpressions for the infrared-divergent contributions of all thesubleading-color L-loop amplitudes up to three loops, and make some conjecturesfor the IR behavior for arbitrary L. We also derive several intriguingrelations between the subleading-color one- and two-loop four-gluon amplitudesand the four-graviton amplitudes of N=8 supergravity. The exact one- andtwo-loop N=8 supergravity amplitudes can be expressed in terms of the one- andtwo-loop N-independent N=4 SYM amplitudes respectively, but the naturalgeneralization to higher loops fails, despite having a simple interpretation interms of the 't Hooft picture. We also find that, at least through two loops,the subleading-color amplitudes of N=4 SYM theory have uniformtranscendentality (as do the leading-color amplitudes). Moreover, the N=4 SYMCatani operators, which express the IR-divergent contributions of loopamplitudes in terms of lower-loop amplitudes, are also shown to have uniformtranscendentality, and to be the maximum transcendentality piece of the QCDCatani operators.

Subleading-color contributions to gluon-gluon scattering in N=4 SYM theory and relations to N=8 supergravity