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

TL;DR

This paper analyzes subleading-color contributions to four-gluon scattering in N=4 SYM, develops explicit IR divergence expressions up to three loops, and explores intriguing relations to N=8 supergravity amplitudes, revealing uniform transcendentality properties.

Contribution

It provides explicit formulas for IR divergences of nonplanar amplitudes up to three loops and uncovers novel relations between SYM and supergravity amplitudes, extending understanding of their structure.

Findings

Explicit IR divergence expressions up to three loops.

Relations between N=4 SYM and N=8 supergravity amplitudes.

Subleading-color amplitudes exhibit uniform transcendentality.

Abstract

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. We also find that, at least through two loops, the subleading-color amplitudes of N=4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the N=4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators.