Approximate Universality of N=4 Super-Yang--Mills One-Loop Amplitudes

TL;DR

This paper uncovers that one-loop amplitudes in N=4 Super-Yang--Mills theory approximately follow a universal form across different helicity configurations, with minimal deviations, especially in NMHV cases.

Contribution

It demonstrates that N=4 SYM one-loop amplitudes are approximately universal and helicity-independent, with high numerical accuracy for NMHV amplitudes.

Findings

Amplitudes follow an approximately universal form with less than 1% error.

Exact universality for MHV amplitudes.

High numerical agreement for six to eight gluon NMHV amplitudes.

Abstract

A study of the colour-ordered one-loop amplitudes in N=4 SYM reveals a surprising property: numerically, the amplitudes have an Approximately Universal form A^{1-loop}_n ~ A^{tree}_n \times U_n, where U_n is helicity independent. This form is exact if the amplitude is a MHV amplitude, but has an "error" which is typically less than 1% for the six, seven and eight gluon NMHV one-loop amplitudes.