  We propose a description of the gluon scattering amplitudes as the inverse
Mellin transforms of the conformal correlators of light operators in
two-dimensional Liouville theory tensored with WZW-like chiral currents on the
celestial sphere. The dimensions of operators are Mellin dual to gluon light
cone energies while their positions are determined by the gluon momentum
directions. Tree-level approximation in Yang-Mills theory corresponds to the
semiclassical limit of Liouville theory. By comparing subleading corrections,
we find $b^2= (8\pi^2)^{-1}\beta_0 \,g^2(M)$, where $b$ is the Liouville
coupling constant, $g(M)$ is the Yang Mills coupling at the renormalization
scale $M$ and $\beta_0$ is the one-loop coefficient of the Yang-Mills beta
function.
