Celestial Liouville Theory for Yang-Mills Amplitudes

TL;DR

This paper explores celestial amplitudes in Yang-Mills theory with a dynamical dilaton, revealing a connection to Liouville theory and providing a new perspective on scattering amplitudes as 2D CFT correlators.

Contribution

It introduces a novel approach to celestial Yang-Mills amplitudes incorporating a dynamical dilaton, linking them to Liouville theory in the semiclassical limit.

Findings

Celestial amplitudes with a spherical dilaton shockwave relate to Liouville correlators.

The amplitudes factorize into current operators and Liouville operators.

Classical Liouville field describes celestial sphere metrics in the semiclassical limit.

Abstract

We consider Yang-Mills theory with the coupling constant and theta angle determined by the vacuum expectation values of a dynamical (complex) dilaton field. We discuss the tree-level N-gluon MHV scattering amplitudes in the presence of a nontrivial background dilaton field and construct the corresponding celestial amplitudes by taking Mellin transforms with respect to the lightcone energies. In this way, we obtain two-dimensional CFT correlators of primary fields on the celestial sphere. We show that the celestial Yang-Mills amplitudes evaluated in the presence of a spherical dilaton shockwave are given by the correlation functions of primary field operators factorized into the holomorphic current operators times the "light" Liouville operators. They are evaluated in the semiclassical limit of Liouville theory (the limit of infinite central charge) and are determined by the classical Liouville field describing metrics on the celestial sphere.