Remarks on celestial amplitudes and Liouville theory

The relation between celestial holography and Liouville field theory is investigated. It is shown that duality relations between different Selberg type integrals appearing in the Coulomb gas realization of Liouville correlation functions induce a series of relations between celestial amplitudes with shifted values of the operators dimensions $\mathrm{\Delta }$. This is a transcript of the talk delivered by the author at the Workshop on Celestial Holography and Asymptotic Symmetries, Santiago de Chile, March 4-6, 2024.