The Construction of Dual-trace Factor in Yang-Mills Theory

TL;DR

This paper develops a systematic method to construct the dual-trace factor in Yang-Mills theory, ensuring it respects key symmetries and relations, advancing the understanding of BCJ duality in gauge theories.

Contribution

It introduces a new systematic construction of the dual-trace factor based on its relation to kinematic numerators, ensuring symmetry properties are maintained.

Findings

Construction respects relabeling symmetry.

Construction can be independently solved using relabeling symmetry.

Advances understanding of BCJ duality in Yang-Mills theory.

Abstract

Recently, a BCJ dual of the color-ordered formula for Yang-Mills amplitude was proposed, where the dual-trace factor satisfies cyclic symmetry and KK-relation. In this paper, we present a systematic construction of the dual-trace factor based on its proposed relations to kinematic numerators in dual-DDM form. We show that the construction presented respects relabeling symmetry. In addition, we show that using relabeling symmetry as conditions, the same construction can be solved independently.