All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes

Abstract

The infrared singularities of gravitational amplitudes are one-loop exact, in that higher-loop divergences are characterized by the exponential of the one-loop divergence. We show that the contributions to SU(N) gauge-theory amplitudes that are most-subleading in the 1/N expansion are also one-loop exact, provided that the dipole conjecture holds. Possible corrections to the dipole conjecture, beginning at three loops, could violate one-loop-exactness, though would still maintain the absence of collinear divergences. We also demonstrate a relation between L-loop four-point N=8 supergravity and most-subleading-color N=4 SYM amplitudes that holds for the two leading IR divergences, O(1/ε^L) and O(1/ε^{L-1}), but breaks down at O(1/ε^{L-2}).

23 pages, no figures

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