Generalized Yang-Mills Theory and Gravity

Abstract

We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.

25 pages, Latex, reference added, minor modification

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• The classical double copy for Taub-NUT spacetime
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• Higher spin gauge theory on fuzzy $S_N^4$
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• BCJ, worldsheet quantum algebra and KZ equations
• Connecting Through Obstruction; Relating Gauge Gravity and String Theory
• Background-Independence from the Perspective of Gauge Theory