Off-shell double copy theories in BV

TL;DR

This paper develops a framework for off-shell double copy constructions in gauge theories using the BV formalism, linking various theories to gravity counterparts and revealing new geometric insights.

Contribution

It introduces a novel off-shell double copy construction within the BV formalism, connecting gauge theories like Chern-Simons and BF theory to gravity theories such as Kodaira-Spencer gravity.

Findings

Double copy construction for off-shell gauge theories established

Connections between gauge theories and gravity theories clarified

Examples include Chern-Simons, BF theory, and Yang-Mills

Abstract

We present a construction of the double copy for gauge theories that exhibit off-shell color-kinematics duality within the Batalin-Vilkovitsky (BV) formalism. As illustrative examples, we consider the double copies of Chern-Simons theory, four-dimensional BF theory, and two-dimensional Yang-Mills theory, and we discuss possible gravity interpretations for these cases. We formalize the construction and demonstrate that Kodaira-Spencer gravity, K\"ahler gravity, and their generalizations, fit naturally within this framework. In particular, Kodaira-Spencer gravity emerges as a gauge theory describing deformations of generalized complex structures, while the double copy of Chern-Simons theory captures the deformation of the Courant bracket.