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CFT3 Realizations and Celestial Representation Theory of the ℒΛw1+∞ Algebra

  • Bin Zhu
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Abstract

We study CFT3 realizations and celestial representations of the ℒΛw1+∞ 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=∞. 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 G3+ 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.

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Cite

BibTeXRIS
BibTeX
@misc{zhu2026cft3,
  title = {{CFT$_3$ Realizations and Celestial Representation Theory of the $\mathcalL_Λw_1+\infty$ Algebra}},
  author = {Bin Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.24968},
  eprint = {2608.24968},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.24968},
}
RIS
TY  - UNPB
TI  - CFT_3 Realizations and Celestial Representation Theory of the ℒ_Λw_1+∞ Algebra
AU  - Bin Zhu
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.24968
UR  - https://arxiv.org/abs/2608.24968
AB  - We study CFT_3 realizations and celestial representations of the ℒ_Λw_1+∞ 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=∞. 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.
ER  -