Comments on Celestial CFT and $AdS_{3}$ String Theory
Abstract
In a recent work, Ogawa et al. (2024) proposed a model for celestial conformal field theory (CFT) based on the -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 , 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 (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 -WZNW model, with emphasis on its connection to Euclidean string theory.
Cite
@article{arxiv.2410.02620,
title = {Comments on Celestial CFT and $AdS_{3}$ String Theory},
author = {Igor Mol},
journal= {arXiv preprint arXiv:2410.02620},
year = {2026}
}
Comments
In the revised version, we have: improved the treatment of helicity and the definitions of celestial vertex operators; clarified the role of the boundary Virasoro central charge; and outlined how a forthcoming manuscript will describe celestial loop amplitudes