TY - JOUR

T1 - Kinematic Lie Algebras From Twistor Spaces

AU - Borsten, Leron

AU - Saemann, Christian

AU - Macrelli, Tommaso

AU - Wolf, Martin

AU - Jurčo, Branislav

AU - Kim, Hyungrok

PY - 2023/6/7

Y1 - 2023/6/7

N2 - We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV◼-algebra structure. Conversely, we show that any theory with a BV◼-algebra structure 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 structure is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. The BV◼-algebra structure 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◼-algebra structures 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 structure. Conversely, we show that any theory with a BV◼-algebra structure 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 structure is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. The BV◼-algebra structure 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◼-algebra structures 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 - https://arxiv.org/abs/2211.13261

M3 - Article

SN - 0031-9007

JO - Physical Review Letters

JF - Physical Review Letters

ER -