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arXiv · 2401.10750

What can abelian gauge theories teach us about kinematic algebras?

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

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Kymani Armstrong-Williams, Silvia Nagy, Chris D. White, Sam Wikeley. 2024-01-19. What can abelian gauge theories teach us about kinematic algebras?. https://arxiv.org/abs/2401.10750

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