A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes

TL;DR

This paper develops a graphic method to analyze identities in multi-trace Einstein-Yang-Mills amplitudes, demonstrating they can be expressed through BCJ relations, extending previous single-trace results.

Contribution

It introduces a refined graphic rule for multi-trace EYM amplitudes and shows these identities decompose into BCJ relations, advancing the understanding of amplitude symmetries.

Findings

Identified new identities for multi-trace EYM amplitudes.

Established a graphic rule for analyzing these amplitudes.

Proved that the identities can be decomposed into BCJ relations.

Abstract

Symmetries of Einstein-Yang-Mills (EYM) amplitudes, together with the recursive expansions, induce nontrivial identities for pure Yang-Mills amplitudes. In the previous work \cite{Hou:2018bwm}, we have already proven that the identities induced from tree level single-trace EYM amplitudes can be precisely expanded in terms of BCJ relations. In this paper, we extend the discussions to those identities induced from all tree level \emph{multi-trace} EYM amplitudes. Particularly, we establish a refined graphic rule for multi-trace EYM amplitudes and then show that the induced identities can be fully decomposed in terms of BCJ relations.