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arXiv · 2604.27736

A perturbative Liouville prescription for the celestial three-gluon amplitude

Grzegorz Biskowski·Franco Ferrari·Marcin R. Piatek·Artur R. Pietrykowski
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Abstract

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.

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Grzegorz Biskowski, Franco Ferrari, Marcin R. Piatek, Artur R. Pietrykowski. 2026-04-30. A perturbative Liouville prescription for the celestial three-gluon amplitude. https://arxiv.org/abs/2604.27736

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