What can abelian gauge theories teach us about kinematic algebras?

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...

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Main Authors: Kymani Armstrong-Williams, Silvia Nagy, Chris D. White, Sam Wikeley
Format: Article
Language:English
Published: SpringerOpen 2024-08-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP08(2024)169
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author Kymani Armstrong-Williams
Silvia Nagy
Chris D. White
Sam Wikeley
author_facet Kymani Armstrong-Williams
Silvia Nagy
Chris D. White
Sam Wikeley
author_sort Kymani Armstrong-Williams
collection DOAJ
description 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.
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spelling doaj-art-6af9abf72fed4124a70e45eb032107d12025-08-20T02:32:53ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024813210.1007/JHEP08(2024)169What can abelian gauge theories teach us about kinematic algebras?Kymani Armstrong-Williams0Silvia Nagy1Chris D. White2Sam Wikeley3Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of LondonDepartment of Mathematical Sciences, Durham UniversityCentre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of LondonDepartment of Physics and Astronomy, Uppsala UniversityAbstract 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.https://doi.org/10.1007/JHEP08(2024)169Duality in Gauge Field TheoriesGauge SymmetryScattering AmplitudesSpace-Time Symmetries
spellingShingle Kymani Armstrong-Williams
Silvia Nagy
Chris D. White
Sam Wikeley
What can abelian gauge theories teach us about kinematic algebras?
Journal of High Energy Physics
Duality in Gauge Field Theories
Gauge Symmetry
Scattering Amplitudes
Space-Time Symmetries
title What can abelian gauge theories teach us about kinematic algebras?
title_full What can abelian gauge theories teach us about kinematic algebras?
title_fullStr What can abelian gauge theories teach us about kinematic algebras?
title_full_unstemmed What can abelian gauge theories teach us about kinematic algebras?
title_short What can abelian gauge theories teach us about kinematic algebras?
title_sort what can abelian gauge theories teach us about kinematic algebras
topic Duality in Gauge Field Theories
Gauge Symmetry
Scattering Amplitudes
Space-Time Symmetries
url https://doi.org/10.1007/JHEP08(2024)169
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