Double Copy From Tensor Products of Metric BV■-Algebras
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2025-02
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Journal Article
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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 L∞-algebra.
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published
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73 (1-2)
Pages / Article No.
2300270
Publisher
Wiley-VCH
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Subject
Batalin-Vilkovisky algebras; kinematic Lie algebra; BV<black square>-algebras; color-kinematics duality; colour-kinematics duality; double copy; Hopf algebras; kinematic L-infinity-algebra; syngamy