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What can abelian gauge theories teach us about kinematic algebras?
- Source :
- Journal of High Energy Physics, Vol 2024, Iss 8, Pp 1-32 (2024)
- Publication Year :
- 2024
- Publisher :
- SpringerOpen, 2024.
-
Abstract
- Abstract 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 subalgebras of the diffeomorphism algebra. By considering certain special subalgebras, 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.
Details
- Language :
- English
- ISSN :
- 10298479
- Volume :
- 2024
- Issue :
- 8
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of High Energy Physics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.6af9abf72fed4124a70e45eb032107d1
- Document Type :
- article
- Full Text :
- https://doi.org/10.1007/JHEP08(2024)169