U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM

TL;DR

This paper proves several fundamental amplitude relations in $ ext{N}=4$ SYM, including U(1)-decoupling, KK, and BCJ relations, using a super-amplitude BCFW recursion approach, confirming conjectures and revealing their interconnectedness.

Contribution

It demonstrates that key amplitude relations in $ ext{N}=4$ SYM can be derived from a unified super-amplitude recursion framework, confirming conjectured BCJ relations.

Findings

Verified the matter fields BCJ relation.

Showed color reflection and U(1)-decoupling are special cases of KK relation.

Established the interrelation of fundamental amplitude relations.

Abstract

We proved the color reflection relation, U(1)-decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relation for color-ordered $\mathcal{N}=4$ Super Yang-Mills theory using $\mathcal{N}=4$ SYM version BCFW recursion relation, which depends only on the general properties of super-amplitudes. This verified the conjectured matter fields BCJ relation. We also show that color reflection relation and U(1)-decoupling relation are special cases of KK relation, if we consider the KK relation as a general relation, then the former two relations come out naturally as the special cases.