Kinematic Lie Algebras From Twistor Spaces

Abstract

We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV${}^{■}$-algebra structure, extending the ideas of arXiv:1912.03110. Conversely, we show that any theory with a BV${}^{■}$-algebra features a kinematic Lie algebra that controls interaction vertices, both on- and off-shell. We explain that the archetypal example of a theory with 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 (CR) 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.

arXiv commentv2: presentation improved, typos fixed, published version

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Cited by in corpus (10)

• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Colour-kinematics duality, double copy, and homotopy algebras
• Field Theory Equivalences as Spans of $L_{\infty }$-algebras
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Ambitwistor Yang-Mills Theory Revisited
• Adjusting Higher Chern-Simons Theory
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group