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

Abstract

Field theories with kinematic Lie algebras, such as field theories featuring colour-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. We explain this perspective, expanding on our previous work and providing many additional mathematical details. We 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, we 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 ten-dimensional supergravity. We also give a homotopy-algebraic perspective on colour-flavour-stripping, obtain a new restricted tensor product over a wide class of bialgebras, and we show that any field theory (even one without colour-kinematics duality) comes with a kinematic $L_{\infty }$-algebra.

arXiv commentv3: 98 pages, references added, typos fixed, version published in Fortschritte der Physik

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Cited by in corpus (4)

• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group
• Extremal Black Holes from Homotopy Algebras