What can abelian gauge theories teach us about kinematic algebras?

Armstrong-Williams, Kymani; Nagy, Silvia; White, Chris D.; Wikeley, Sam

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.

Citation

Armstrong-Williams, K., Nagy, S., White, C. D., & Wikeley, S. (2024). What can abelian gauge theories teach us about kinematic algebras?. Journal of High Energy Physics, 2024(8), Article 169. https://doi.org/10.1007/jhep08%282024%29169

• Journal Article Type: Article
• Acceptance Date: Jul 29, 2024
• Online Publication Date: Aug 21, 2024
• Publication Date: 2024-08
• Deposit Date: Aug 29, 2024
• Publicly Available Date: Aug 29, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 8
• Article Number: 169
• DOI: https://doi.org/10.1007/jhep08%282024%29169
• Keywords: Duality in Gauge Field Theories, Scattering Amplitudes, Space-Time Symmetries, Gauge Symmetry
• Public URL: https://durham-repository.worktribe.com/output/2767972