Non-abelian infrared divergences on the celestial sphere

TL;DR

This paper explores the structure of infrared divergences in non-abelian gauge theories on the celestial sphere, revealing a simple form of the colour operator and connecting it to a conformal field theory framework.

Contribution

It demonstrates that the infrared divergence operator can be expressed as a correlator in a conformal field theory of Lie-algebra-valued free bosons on the celestial sphere, generalizing previous abelian results.

Findings

Colour-dipole contributions have a simple, all-orders expression in celestial coordinates.

Infrared operator correlates with vertex operators in a conformal field theory.

The theory correctly predicts collinear limits and soft radiation factorization.

Abstract

We consider the infrared factorisation of non-abelian multi-particle scattering amplitudes, and we study the form of the universal colour operator responsible for infrared divergences, when expressed in terms of coordinates on the `celestial sphere' intersecting the future light-cone at asymptotic distances. We find that colour-dipole contributions to the infrared operator, to all orders in perturbation theory, have a remarkably simple expression in these coordinates, with scale and coupling dependence factorised from kinematics and colour. Generalising earlier suggestions in the abelian theory, we then show that the infrared operator can be computed as a correlator of vertex operators in a conformal field theory of Lie-algebra-valued free bosons on the celestial sphere. We verify by means of the OPE that the theory correctly predicts the all-order structure of collinear limits, and the tree-level factorisation of soft real radiation.