Yang-Mills as a Liouville Theory

TL;DR

This paper connects gluon scattering amplitudes in Yang-Mills theory to conformal correlators in Liouville theory on the celestial sphere, revealing a deep link between gauge theory and two-dimensional conformal field theories.

Contribution

It introduces a novel framework relating gluon scattering amplitudes to Liouville conformal correlators, establishing a semiclassical limit correspondence and deriving a relation between Liouville and Yang-Mills couplings.

Findings

Gluon amplitudes as inverse Mellin transforms of Liouville correlators

Semiclassical limit of Liouville theory corresponds to tree-level Yang-Mills

Derived relation between Liouville coupling and Yang-Mills coupling constants

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.