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/epsilon(L)) and O(1/epsilon(L-1)), but breaks down at O(1/epsilon(L-2)).