CFT$_3$ Realizations and Celestial Representation Theory of the $\mathcal{L}_Λw_{1+\infty}$ Algebra
Year: 2026
Type: preprint
Abstract: 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 under its closure assumptions and check prescribed iterated limits of the frequency kernel. In the dimension-completed celestial hard-graviton representation, a closed raising subalgebra annihilates $G_3^+$ exactly. We construct two nonzero singular descendants in its induced module and prove that both vanish in the celestial realization. They implement the finite-spin condition and massless spin-two shortening of the generated highest-weight sector. The nonzero-$Λ$ quadratic Casimir has eigenvalue three throughout the hard family. The null descendants and low-spin Ward identities yield ordered differential--difference equations for celestial correlators.
Source: arXiv (Cornell University)
Author: Zhu, Bin
Institution: Nankai University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G1710298378
OpenAlex ID: W7204462127