CFT$_3$的实现与$\boldsymbol{\text{celestial}}$表示理论：$\boldsymbol{\text{mathcal{L}}_\boldsymbol{\text{Λ}}w_{1+\boldsymbol{\text{infty}}}}$代数
CFT$_3$ Realizations and Celestial Representation Theory of the $\mathcal{L}_Λw_{1+\infty}$ Algebra
- School of Physics, Nankai University（南开大学物理学院）
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AI总结：
本研究针对三维共形场论（CFT₃），探讨了𝒲_Λw_{1+∞}代数的实现与天体表示理论，通过自由标量、狄拉克理论及临界O(N)模型的相关分析，确定天体硬引力子模的Δ=3，推导了天体关联函数的相容微分-差分方程。
AI中文摘要：
我们研究$\text{CFT}_3$的实现与$\boldsymbol{\text{celestial}}$表示理论：$\boldsymbol{\text{mathcal{L}}_\boldsymbol{\text{Λ}}w_{1+\boldsymbol{\text{infty}}}}$代数。自由标量理论与狄拉克理论给出相同的单粒子光锥作用量，该作用量可推广到$N=\boldsymbol{\text{infty}}$时的临界$O(N)$模型；经正则化的矩在本文研究的大但有限$N$关联函数中重现了两两代数。在$\boldsymbol{\text{celestial}}$硬引力子模中，投影零条件唯一选出$\boldsymbol{\text{Δ}}=3$，闭合升子代数可精确湮灭$G^+_3$；非零$\boldsymbol{\text{Λ}}$二次卡西米尔在整个硬模中本征值为3，精确湮灭子与低自旋沃德恒等式给出$\boldsymbol{\text{celestial}}$关联函数的相容微分-差分方程。
英文摘要：
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.
