Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality

TL;DR

This paper constructs an effective Yang-Mills Lagrangian that inherently encodes BCJ duality, simplifying the derivation of BCJ numerators and providing insights into gauge theory structures.

Contribution

It introduces a systematic method to build an effective Lagrangian with manifest BCJ duality, including non-local terms, bridging the gap between standard Yang-Mills theory and BCJ properties.

Findings

Effective Lagrangian produces BCJ numerators automatically.

The difference between standard and effective Lagrangian simplifies to zero.

The approach clarifies the structure of gauge theories with BCJ duality.

Abstract

The BCJ decomposition is a highly non-trivial property of gauge theories. In this paper we systematically construct an effective Lagrangian, whose Feynman rules automatically produce the BCJ numerators. The effective Lagrangian contains non-local terms. The difference between the standard Yang-Mills Lagrangian and the effective Lagrangian simplifies to zero.