Celestial Gluon Amplitudes from the Outside In

TL;DR

This paper connects celestial gluon amplitudes with 2D correlation functions in self-dual Yang-Mills, deriving conditions for scalar sources and exploring dualities, including examples from Liouville theory and free fields.

Contribution

It introduces a novel framework linking celestial gluon amplitudes to 2D correlation functions, providing explicit examples and discussing dualities beyond the decoupling limit.

Findings

Derived conditions for scalar sources reproducing amplitudes

Constructed gluon operators from Liouville theory vertex operators

Identified a bulk dual to the boundary Kac-Moody algebra

Abstract

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D `gluon' operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.