Title: Comments on Celestial CFT and $AdS_{3}$ String Theory Show Chinese title

Title: 关于天体 CFT 和$AdS_{3}$字符串理论的评论

Abstract: In a recent work, Ogawa et al. (2024) proposed a model for celestial conformal field theory (CFT) based on the $H_{3}^{+}$-Wess-Zumino-Novikov-Witten (WZNW) model. In this paper, we extend the model advanced by Ogawa et al. (2024), demonstrating how it can holographically generate tree-level MHV scattering amplitudes for both gluons and gravitons when analytically continued to the ultra-hyperbolic Klein space $\mathbf{R}_{2}^{2}$, thereby offering an alternative to celestial Liouville theory. We construct a holographic dictionary in which vertex operators and conformal primaries in celestial CFT are derived from their worldsheet counterparts in Euclidean $AdS_{3}$ (bosonic) string theory. Within this dictionary, we derive the celestial stress-energy tensor, compute the two- and three-point functions, and determine the celestial operator product expansion (OPE). Additionally, we derive a system of partial differential equations that characterises the celestial amplitudes of our model, utilising the Knizhnik--Zamolodchikov (KZ) equations and worldsheet Ward identities. In the Appendix, we provide a concise introduction to the $H_{3}^{+}$-WZNW model, with emphasis on its connection to Euclidean $AdS_{3}$ string theory. Show Chinese abstract

Abstract: 在近期的一项工作中，Ogawa 等人（2024）基于$H_{3}^{+}$-Wess-Zumino-Novikov-Witten (WZNW) 模型提出了一个天体共形场论 (CFT) 的模型。本文扩展了 Ogawa 等人（2024）提出的模型，展示了当将其解析延拓到超双曲 Klein 空间$\mathbf{R}_{2}^{2}$时，该模型如何全息生成树级 MHV 散射振幅，适用于胶子和引力子，从而为天体 Liouville 理论提供了一种替代方案。我们构建了一个全息字典，在其中天体 CFT 中的顶点算符和共形主元从欧几里得$AdS_{3}$（玻色子）弦理论中的世界面对应物推导而来。在这个字典内，我们推导出天体能量动量张量，计算二点函数和三点函数，并确定天体算符积展开 (OPE)。此外，我们利用 Knizhnik--Zamolodchikov (KZ) 方程和世界面 Ward 恒等式，推导出描述我们模型的天体振幅的一组偏微分方程。在附录中，我们简要介绍了$H_{3}^{+}$-WZNW 模型，并着重讨论了它与欧几里得$AdS_{3}$弦理论的联系。