What can abelian gauge theories teach us about kinematic algebras?
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917570657910784 |
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| author | Armstrong-Williams, Kymani Nagy, Silvia White, Chris D. Wikeley, Sam |
| author_facet | Armstrong-Williams, Kymani Nagy, Silvia White, Chris D. Wikeley, Sam |
| contents | The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subgroups of the diffeomorphism algebra. By considering certain special subgroups, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10750 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | What can abelian gauge theories teach us about kinematic algebras? Armstrong-Williams, Kymani Nagy, Silvia White, Chris D. Wikeley, Sam High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subgroups of the diffeomorphism algebra. By considering certain special subgroups, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras. |
| title | What can abelian gauge theories teach us about kinematic algebras? |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2401.10750 |