The fact that infrared divergences are long-distance effects has recently been formulated
in a new language, involving asymptotic symmetries of scattering amplitudes on the
`celestial sphere' intersecting the light-cone at infinite time. Using this technology, I will
consider the infrared factorisation of non-abelian multi-particle scattering amplitudes,
mostly focusing on colour-dipole contributions, and I will show that the infrared factor
has a remarkably simple expression in celestial coordinates, with scale and coupling
dependence factorised from kinematics and colour. Generalising earlier suggestions
in the abelian theory, I will then show that the infrared factor can be computed as a
correlator of vertex operators in a conformal field theory of Lie-algebra-valued free
bosons on the celestial sphere. The same conformal theory correctly predicts the
all-order structure of collinear limits, and the tree-level factorisation of soft real radiation.
on-line via ZOOM