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 - Funding Information:
H. K. and C. S. were supported by the Leverhulme Research Project Grant No. RPG-2018-329. B. J. was supported by the GAČR Grant No. EXPRO 19-28268X.
Publisher Copyright:
© 2023 authors. Published by the American Physical Society.

PY - 2023/7/28

Y1 - 2023/7/28

N2 - 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.

AB - 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.

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

C2 - 37566835

AN - SCOPUS:85166737561

SN - 0031-9007

VL - 131

JO - Physical Review Letters

JF - Physical Review Letters

IS - 4

M1 - 041603

ER -