Kinematic Lie Algebras from Twistor Spaces

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

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
46 Downloads (Pure)


We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV▪-algebra, extending the ideas of Reiterer [A homotopy BV algebra for Yang-Mills and color-kinematics, arXiv:1912.03110.]. Conversely, we show that any theory with a BV▪-algebra features a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explain that the archetypal example of a theory with a BV▪-algebra is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. The BV▪-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show that holomorphic and Cauchy-Riemann Chern-Simons theories come with BV▪-algebras and that, on the appropriate twistor spaces, these theories organize and identify kinematic Lie algebras for self-dual and full Yang-Mills theories, as well as the currents of any field theory with a twistorial description. We show that this result extends to the loop level under certain assumptions.

Original languageEnglish
Article number041603
JournalPhysical Review Letters
Issue number4
Early online date26 Jul 2023
Publication statusPublished - 28 Jul 2023

ASJC Scopus subject areas

  • General Physics and Astronomy


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