Comments on Celestial CFT and $AdS_{3}$ String Theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910217548070912 |
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| author | Mol, Igor |
| author_facet | Mol, Igor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comments on Celestial CFT and $AdS_{3}$ String Theory Mol, Igor High Energy Physics - 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 $\mathbf{R}_{2}^{2}$, 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. |
| title | Comments on Celestial CFT and $AdS_{3}$ String Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.02620 |