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arXiv · 2608.24968

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

Bin Zhu
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Abstract

We study CFT$_3$ realizations and celestial representations of the $\mathcal{L}_{\Lambda}w_{1+\infty}$ algebra. Free scalar and Dirac theories yield the same one-particle light-ray action. This action extends to the critical $O(N)$ model at $N=\infty$, while regulated moments reproduce the pairwise algebra in the large-but-finite-$N$ correlators studied here. In the celestial hard-graviton module, the projected null conditions select $\Delta=3$ uniquely, and a closed raising subalgebra annihilates $G^+_3$ exactly. The nonzero-$\Lambda$ quadratic Casimir has eigenvalue three throughout the hard module, and the exact annihilators and low-spin Ward identities give compatible differential-difference equations for celestial correlators.

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Bin Zhu. 2026-08-25. CFT$_3$ Realizations and Celestial Representation Theory of the $\mathcal{L}_{\Lambda}w_{1+\infty}$ Algebra. https://arxiv.org/abs/2608.24968

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