Non-abelian infrared divergences on the celestial sphere

TL;DR

The paper reframes infrared divergences in massless non-abelian gauge theories as a celestial-sphere problem, showing that colour-dipole contributions factorise with a universal scale-dependent function $K$ and can be computed as correlators of Lie-algebra-valued free-boson vertex operators. The proposed 2D conformal field theory reproduces the all-order dipole structure and matches soft and collinear limits via the OPE, providing a holographic route to IR factorisation. It also discusses the connection to conformal cross-ratios controlling higher-order corrections and outlines open questions, including how to incorporate scale and quadrupole corrections, and how to extend to massive cases. Overall, the work suggests a promising celestial CFT framework to understand IR physics in gauge theories and motivates further development of the dictionary between 4D IR dynamics and 2D celestial data.

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.