On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

TL;DR

The paper investigates whether the planar, highly structured behavior of N=4 SYM extends beyond the planar limit by analyzing the two-loop four-point amplitude. It develops a dlog (logarithmic differential form) representation for the planar double-box and, after a numerator deformation, for the non-planar double-box, showing both contributions can be cast into logarithmic forms and exhibit maximal transcendentality. A key result is that the modified non-planar integrals have leading singularities corresponding to Parke-Taylor denominators, suggesting deeper symmetries despite non-planarity. The findings support the conjecture that logarithmic, pole-at-infinity structures persist beyond the planar limit and motivate exploration of higher loops and N=8 SUGRA analogues using on-shell/Grassmannian methods.

Abstract

We present evidence that loop amplitudes in maximally supersymmetric $\mathcal{N}=4$ Yang-Mills (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full $\mathcal{N}=4$ SYM has only logarithmic singularities and is free of any poles at infinity---properties closely related to uniform transcendentality and the UV-finiteness of the theory. We also briefly comment on implications for maximal ($\mathcal{N}=8$) supergravity.