Comments on Celestial CFT and AdS_{3} String Theory

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 R22, 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 AdS3 (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 AdS3 string theory.