Double Copy from Tensor Products of Metric BV^■-algebras

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 L_∞-algebra.