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 b2=(8π2)−1β0g2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and β0 is the one-loop coefficient of the Yang-Mills beta function.