What can abelian gauge theories teach us about kinematic algebras?

被引:4
作者
Armstrong-Williams, Kymani [1 ]
Nagy, Silvia [2 ]
White, Chris D. [1 ]
Wikeley, Sam [3 ]
机构
[1] Queen Mary Univ London, Ctr Theoret Phys, Dept Phys & Astron, 327 Mile End Rd, London E1 4NS, England
[2] Univ Durham, Dept Math Sci, Durham DH1 3LE, England
[3] Uppsala Univ, Dept Phys & Astron, Box 516, S-75120 Uppsala, Sweden
来源
JOURNAL OF HIGH ENERGY PHYSICS | 2024年 / 08期
基金
英国科学技术设施理事会; 英国工程与自然科学研究理事会;
关键词
Duality in Gauge Field Theories; Gauge Symmetry; Scattering Amplitudes; Space-Time Symmetries;
D O I
10.1007/JHEP08(2024)169
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
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.
引用
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页数:32
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