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 -algebra.
Item Type | Article |
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Additional information | © 2024 The Author(s). Fortschritte der Physik published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, https://creativecommons.org/licenses/by/4.0/ |
Keywords | kinematic l∞‐algebra, batalin‐vilkovisky algebras, colour‐kinematics duality, double copy, color‐kinematics duality, syngamy, kinematic lie algebra, hopf algebras, bv ■ ‐algebras, color-kinematics duality, batalin-vilkovisky algebras, bv -algebras, kinematic l -algebra, colour-kinematics duality, general physics and astronomy |
Date Deposited | 15 May 2025 15:44 |
Last Modified | 31 May 2025 00:46 |