A perturbative Liouville prescription for the celestial three-gluon amplitude
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917450652581888 |
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| author | Biskowski, Grzegorz Ferrari, Franco Piatek, Marcin R. Pietrykowski, Artur R. |
| author_facet | Biskowski, Grzegorz Ferrari, Franco Piatek, Marcin R. Pietrykowski, Artur R. |
| contents | We study the celestial three-gluon amplitude in a dilaton background through the Mellin-Liouville formulation proposed by Stieberger, Taylor and Zhu (STZ). The original map contains an ambiguity in the identification of Liouville and Mellin variables; we resolve it by requiring global conformal covariance and compatibility with the semiclassical expansion of Liouville theory. This uniquely fixes the operator normalization and the parameter dictionary, and leads to a controlled expansion in the Liouville coupling $b$. Starting from the full Liouville DOZZ three-point function, we derive the leading and first subleading terms in the $b^2$ expansion. The leading term reproduces the tree-level Yang-Mills amplitude in the small total momentum limit, as anticipated in the STZ proposal. The one-loop correction can be written in closed form using modified Bessel functions, and its soft limit exhibits a clear separation into geometric and logarithmic contributions. The resulting framework extends the STZ proposal to finite-$b$ corrections in a consistent and computable way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A perturbative Liouville prescription for the celestial three-gluon amplitude Biskowski, Grzegorz Ferrari, Franco Piatek, Marcin R. Pietrykowski, Artur R. High Energy Physics - Theory We study the celestial three-gluon amplitude in a dilaton background through the Mellin-Liouville formulation proposed by Stieberger, Taylor and Zhu (STZ). The original map contains an ambiguity in the identification of Liouville and Mellin variables; we resolve it by requiring global conformal covariance and compatibility with the semiclassical expansion of Liouville theory. This uniquely fixes the operator normalization and the parameter dictionary, and leads to a controlled expansion in the Liouville coupling $b$. Starting from the full Liouville DOZZ three-point function, we derive the leading and first subleading terms in the $b^2$ expansion. The leading term reproduces the tree-level Yang-Mills amplitude in the small total momentum limit, as anticipated in the STZ proposal. The one-loop correction can be written in closed form using modified Bessel functions, and its soft limit exhibits a clear separation into geometric and logarithmic contributions. The resulting framework extends the STZ proposal to finite-$b$ corrections in a consistent and computable way. |
| title | A perturbative Liouville prescription for the celestial three-gluon amplitude |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.27736 |