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

Understand

We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory.

• Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L.
• We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of N=8 supergravity.
• The exact one- and two-loop N=8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent N=4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture.