  We consider Yang-Mills theory with the coupling constant and theta angle
determined by the vacuum expectation values of a dynamical (complex) dilaton
field. We discuss the tree-level N-gluon MHV scattering amplitudes in the
presence of a nontrivial background dilaton field and construct the
corresponding celestial amplitudes by taking Mellin transforms with respect to
the lightcone energies. In this way, we obtain two-dimensional CFT correlators
of primary fields on the celestial sphere. We show that the celestial
Yang-Mills amplitudes evaluated in the presence of a spherical dilaton
shockwave are given by the correlation functions of primary field operators
factorized into the holomorphic current operators times the "light" Liouville
operators. They are evaluated in the semiclassical limit of Liouville theory
(the limit of infinite central charge) and are determined by the classical
Liouville field describing metrics on the celestial sphere.
