The Kinematic Algebra From the Self-Dual Sector

Ricardo Monteiro, Donal O'Connell

Research output: Contribution to journalArticlepeer-review


We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.
Original languageEnglish
Article number7
Number of pages29
JournalJournal of High Energy Physics
Issue number7
Publication statusPublished - 12 May 2011


  • hep-th


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