Off-shell color-kinematics duality from codifferentials

TL;DR

This paper explores the off-shell color-kinematics duality within the BV formalism, providing a general framework and examples like Chern-Simons, BF theory, and 2D Yang-Mills, showing the duality's geometric origin.

Contribution

It introduces a general framework for off-shell color-kinematics duality using the BV formalism and demonstrates this duality in new examples beyond flat space.

Findings

Off-shell color-kinematics duality exists in Chern-Simons, BF, and 2D Yang-Mills theories.

The duality is linked to geometric structures that extend to curved spaces.

The BV formalism provides a natural setting to study the duality off-shell.

Abstract

We examine the color-kinematics duality within the BV formalism, highlighting its emergence as a feature of specific gauge-fixed actions. Our goal is to establish a general framework for studying the duality while investigating straightforward examples of off-shell color-kinematics duality. In this context, we revisit Chern-Simons theory as well as introduce new examples, including BF theory and 2D Yang-Mills theory, which are shown to exhibit the duality off-shell. We emphasize that the geometric structures responsible for flat-space color-kinematics duality appear for general curved spaces as well.