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

TL;DR

This paper demonstrates that most-subleading-color gauge-theory amplitudes are one-loop exact under certain conditions, revealing a parallel with gravitational amplitude divergences and exploring their relation to supergravity.

Contribution

It establishes the one-loop exactness of most-subleading-color amplitudes in SU(N) gauge theories assuming the dipole conjecture, and relates these to supergravity divergences.

Findings

Most-subleading-color amplitudes are one-loop exact if the dipole conjecture holds.

A relation between supergravity and gauge-theory IR divergences is identified.

The one-loop exactness may be violated at three loops if the dipole conjecture fails.

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}).