On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

TL;DR

This paper investigates the singularity structure of loop amplitudes in maximally supersymmetric $ ext{N}=4$ SYM beyond the planar limit, revealing they share key properties with the planar theory up to two loops.

Contribution

It provides evidence that non-planar four-particle amplitudes in $ ext{N}=4$ SYM exhibit only logarithmic singularities and lack poles at infinity, extending planar results.

Findings

Amplitudes have only logarithmic singularities.

Amplitudes are free of poles at infinity.

Properties suggest uniform transcendentality and UV-finiteness.

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.