Double Copy From Tensor Products of Metric BV^■‐Algebras

Abstract Field theories with kinematic Lie algebras, such as field theories featuring color–kinematics duality, possess an underlying algebraic structure known as BV ■ ‐algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV ■ ‐algebra. The authors explain this perspective, expanding on our previous work and providing many additional mathematical details. The authors also show how the tensor product of two metric BV ■ ‐algebras yields the action of a new syngamy field theory, a construction which comprises the familiar double copy construction. As examples, the authors discuss various scalar field theories, Chern–Simons theory, self‐dual Yang–Mills theory, and the pure spinor formulations of both M2‐brane models and supersymmetric Yang–Mills theory. The latter leads to a new cubic pure spinor action for 10‐dimensional supergravity. A homotopy‐algebraic perspective on colour–flavour‐stripping is also given, obtain a new restricted tensor product over a wide class of bialgebras, and it is also show that any field theory (even one without colour–kinematics duality) comes with a kinematic ‐algebra.