Gravity From a Color Symmetry II: Celestial Color Kinematics for Mass and Spin

A realization of gravitational amplitudes based in the large $N$ limit of a certain 2d $SU(N)$ Kac-Moody theory has been recently proposed. We relate this proposal to Color Kinematics (CK) duality and present an extension to EFT amplitudes for matter particles with any mass and spin. In particular, we recast these EFT amplitudes as celestial correlation functions and show they posses a chiral $w_{1+\infty}$ symmetry algebra if they are minimally coupled in the bulk. Massive states lead to an off-shell 1-parameter deformation of the algebra. Finally, we argue that in the limit $S\to\infty$ these states correspond to the Kerr black hole and we rediscover a classical $w_{1+\infty}$ action of Penrose.