Tree-Level Color-Kinematics Duality from Pure Spinor Actions

• Published in: arXiv.org
• Main Authors: Borsten, Leron, Jurco, Branislav, Kim, Hyungrok, Macrelli, Tommaso, Saemann, Christian, Wolf, Martin
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.12.2023
• Subjects: Algebra; Color; Gauge theory; Kinematics; Lie groups; Mathematics - Mathematical Physics; Physics - High Energy Physics - Theory; Physics - Mathematical Physics; Regularization; Yang-Mills theory
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2303.13596

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.