Yang-Mills as a Liouville Theory

Abstract

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.

10 pages