Tree-level color-kinematics duality from pure spinor actions

Leron Borsten, Branislav Jurco, Hyungrok Kim, Tommaso Macrelli, Christian Saemann, Martin Wolf

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We prove that the tree-level scattering amplitudes for (super) Yang-Mills theory in arbitrary dimensions and for M2-brane models exhibit color-kinematics (CK) duality. Our proof for Yang-Mills theory substantially simplifies existing ones in that it relies on the action alone and does not involve any computation; the proof for M2-brane models establishes this result for the first time. Explicitly, we combine the facts that Chern-Simons-type theories naturally come with a kinematic Lie algebra and that both Yang-Mills theory and M2-brane models are of Chern-Simons form when formulated in pure spinor space, extending previous work on Yang-Mills currents arXiv:2108.11708. Our formulation also provides explicit kinematic Lie algebras for the theories under consideration in the form of diffeomorphisms on pure spinor space. The pure spinor formulation of CK-duality is based on ordinary, cubic vertices, but we explain how ordinary CK-duality relates to notions of quartic-vertex 3-Lie algebra CK-duality for M2-brane models previously discussed in the literature.
Original languageEnglish
Article number126012
Pages (from-to)1-10
Number of pages10
JournalPhysical Review D
Issue number12
Publication statusPublished - 14 Dec 2023


  • hep-th
  • math-ph
  • math.MP


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