Double Copy from Tensor Products of Metric BV${}^{\color{gray} \blacksquare}$-algebras
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916659778813952 |
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| author | Borsten, Leron Jurco, Branislav Kim, Hyungrok Macrelli, Tommaso Saemann, Christian Wolf, Martin |
| author_facet | Borsten, Leron Jurco, Branislav Kim, Hyungrok Macrelli, Tommaso Saemann, Christian Wolf, Martin |
| contents | Field theories with kinematic Lie algebras, such as field theories featuring colour-kinematics duality, possess an underlying algebraic structure known as BV${}^{\color{gray} \blacksquare}$-algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV${}^{\color{gray} \blacksquare}$-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${}^{\color{gray} \blacksquare}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02563 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double Copy from Tensor Products of Metric BV${}^{\color{gray} \blacksquare}$-algebras Borsten, Leron Jurco, Branislav Kim, Hyungrok Macrelli, Tommaso Saemann, Christian Wolf, Martin High Energy Physics - Theory Mathematical Physics Field theories with kinematic Lie algebras, such as field theories featuring colour-kinematics duality, possess an underlying algebraic structure known as BV${}^{\color{gray} \blacksquare}$-algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV${}^{\color{gray} \blacksquare}$-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${}^{\color{gray} \blacksquare}$-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. |
| title | Double Copy from Tensor Products of Metric BV${}^{\color{gray} \blacksquare}$-algebras |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2307.02563 |