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

TL;DR

The paper analyzes infrared divergences of most-subleading-color gauge-theory amplitudes and draws a striking parallel with gravity: if the dipole conjecture holds, these amplitudes are one-loop exact, with all higher-loop IR divergences determined by the one-loop result via exponentiation of the one-loop soft anomalous dimension. It provides explicit four-point formulas for the all-loop IR structure, investigates potential three-loop corrections to the dipole formula that could spoil this exactness, and establishes a correspondence between the leading IR divergences of L-loop ${\cal N}=8$ supergravity and most-subleading-color ${\cal N}=4$ SYM amplitudes, while showing that the precise finite-part relations break down beyond leading orders. The work highlights deep connections between gauge and gravity theories in the IR and outlines how corrections to the dipole conjecture would modify these relations, pointing to important tests at three loops and higher-point amplitudes. Overall, the results illuminate how color-subleading sectors can mirror gravitational IR behavior and constrain the structure of multi-loop amplitudes in gauge theories.

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}).