Off-shell color-kinematics duality for Chern-Simons

Many gauge theories possess a hidden duality between color and kinematics in their on-shell scattering amplitudes. An open problem is to formulate an off-shell realization of the duality, thus manifesting kinematic algebra. We show that 3D Chern-Simons (CS) theory Lorenz obeys color-kinematics duality. This holds both for field BRST ghosts, manifest Feynman rules. A algebra can be formulated through second-order differential operator (Poisson bracket) acting on fields, it corresponds volume-preserving diffeomorphisms, generated by functions gauge. consider several admissible double-copy constructions CS with Yang-Mills theory, higher-derivative (DF)^2 or itself. To obtain non-vanishing amplitudes, we deform pure including maximum amount adjoint matter respects gives new formulation N=4 CS-matter fields unusual statistics. argue color-stripped tree amplitudes this are equivalent those Gaiotto-Witten bi-fundamental matter. further double copy itself maximally supersymmetric N=8 Dirac-Born-Infeld theory.