2025/09/25 by Franco Ferrari, Ferrari, Franco, Marcin Pia̧tek +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2509.21182
openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a systematic small-b expansion of the Liouville DOZZ three-point structure constant in the light-operator regime \(αi=bσi\) as \(b→0\). In this limit, the exact DOZZ function factorizes into a prefactor \(\cal P(b;σ1,σ2,σ3)\) and a power series in \(b2\): C(bσ1,bσ2,bσ3)=\cal P(b;σi)[1+∑n≥1b2n Ωn(σ1,σ2,σ3)]. Using Thorn's asymptotic expansion of the \(Υb\)-function we derive closed-form expressions for the leading coefficients \(Ωn(σi)\) and show that each \(Ωn\) is a symmetric polynomial in the variables \(σi\). Our expansion provides explicit perturbative corrections to the semiclassical Liouville three-point function and therefore supplies a practical tool for applications in celestial holography, in particular, for generating loop-level corrections to the tree-level three-gluon scattering amplitude. Finally, we formulate a perturbative Liouville program for celestial amplitudes and outline directions for further development.