Yang-Mills as a Liouville theory
Stephan Stieberger (Max–Planck–Institut für Physik, Werner–Heisenberg–Institut, München, Germany); Tomasz R. Taylor (Department of Physics, Northeastern University, Boston, USA, Faculty of Physics, University of Warsaw, ul. Pasteura 5, Warsaw, Poland); Bin Zhu (School of Mathematics, Maxwell Institute for Mathematical Sciences, University of Edinburgh, UK)
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 , where b is the Liouville coupling constant, is the Yang Mills coupling at the renormalization scale M and is the one-loop coefficient of the Yang-Mills beta function.
