CFT$_3$ Realizations and Celestial Representation Theory of the $\mathcal{L}_Λw_{1+\infty}$ Algebra

We study CFT$_3$ realizations and celestial representations of the $\mathcal{L}_Λw_{1+\infty}$ algebra. Free scalar and Dirac theories yield the same one-particle light-ray action. This action extends to the critical $O(N)$ model at $N=\infty$. At large but finite $N$, we use the light-ray algebra u