Comments on Celestial CFT and $AdS_{3}$ String Theory

Abstract based on: arxiv.org/abs/2410.02620

In a recent work, \citet{ogawa2024celestial} 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 \citet{ogawa2024celestial},
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.

This talk is structured as follows. In Section \ref{sec:Holographic-Reconstruction-of},
we begin by stating the postulates of our holographic dictionary,
and move to the derivation of its consequences, starting with the
holographic derivation of tree-level MHV amplitudes for both pure
Yang-Mills theory and Einstein's gravity. In Section \ref{sec:Correlation-Functions,-Operator},
we will demonstrate how our construction uniquely determines the two-
and three-point functions as well as the celestial OPE. Additionally,
we will examine a system of partial differential equations characterising
the celestial amplitudes, derived from our holographic dictionary
in frequency space, and, in Section \ref{sec:Discussion}, we summarise
our findings and discuss potential avenues for further research stemming
from this work.