TY - JOUR

T1 - Kinematic Lie Algebras From Twistor Spaces

AU - Borsten, Leron

AU - Jurčo, Branislav

AU - Kim, Hyungrok

AU - Macrelli, Tommaso

AU - Saemann, Christian

AU - Wolf, Martin

N1 - © The Author(s). Published by the American Physical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/

PY - 2023/7/28

Y1 - 2023/7/28

N2 - We analyze theories with color-kinematics duality from an algebraic perspective and find that any suchtheory 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▪-algebrafeatures a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explainthat the archetypal example of a theory with a BV▪-algebra is Chern-Simons theory, for which the resultingkinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. TheBV▪-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show thatholomorphic and Cauchy-Riemann Chern-Simons theories come with BV▪-algebras and that, on theappropriate twistor spaces, these theories organize and identify kinematic Lie algebras for self-dual and fullYang-Mills theories, as well as the currents of any field theory with a twistorial description. We show thatthis result extends to the loop level under certain assumptions

AB - We analyze theories with color-kinematics duality from an algebraic perspective and find that any suchtheory 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▪-algebrafeatures a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explainthat the archetypal example of a theory with a BV▪-algebra is Chern-Simons theory, for which the resultingkinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. TheBV▪-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show thatholomorphic and Cauchy-Riemann Chern-Simons theories come with BV▪-algebras and that, on theappropriate twistor spaces, these theories organize and identify kinematic Lie algebras for self-dual and fullYang-Mills theories, as well as the currents of any field theory with a twistorial description. We show thatthis result extends to the loop level under certain assumptions

UR - https://arxiv.org/abs/2211.13261

UR - http://www.scopus.com/inward/record.url?scp=85166737561&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.131.041603

DO - 10.1103/PhysRevLett.131.041603

M3 - Article

SN - 0031-9007

VL - 131

SP - 1

EP - 7

JO - Physical Review Letters

JF - Physical Review Letters

IS - 4

M1 - 041603

ER -