TY - JOUR
T1 - Double Copy from Tensor Products of Metric BV■-algebras
AU - Borsten, Leron
AU - Jurčo, Branislav
AU - Kim, Hyungrok
AU - Macrelli, Tommaso
AU - Saemann, Christian
AU - Wolf, Martin
N1 - Publisher Copyright:
© 2024 The Author(s). Fortschritte der Physik published by Wiley-VCH GmbH.
PY - 2025/2
Y1 - 2025/2
N2 - 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.
AB - 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.
KW - Batalin-Vilkovisky algebras
KW - BV■-algebras
KW - color-kinematics duality
KW - colour-kinematics duality
KW - double copy
KW - Hopf algebras
KW - kinematic L∞-algebra
KW - kinematic Lie algebra
KW - syngamy
UR - http://www.scopus.com/inward/record.url?scp=85208916313&partnerID=8YFLogxK
U2 - 10.1002/prop.202300270
DO - 10.1002/prop.202300270
M3 - Article
SN - 0015-8208
VL - 73
JO - Fortschritte der Physik
JF - Fortschritte der Physik
IS - 1-2
M1 - 2300270
ER -