A celestial viewpoint on infrared divergences in QCD

Abstract

Non-abelian infrared radiation can be seen as both a practical ingredient for QCD phenomenology and a window on the long-distance structure of gauge theories. During the last decade, a novel viewpoint was developed on infrared phenomena: soft currents are seen as arising from asymptotic symmetries realised on the celestial sphere, and soft colour correlations similarly emerge from a two-dimensional conformal field theory on the sphere. In this contribution, we briefly review the status of this approach. We begin with the standard bulk picture, presenting the infrared factorisation of massless scattering amplitudes, and then we show how universal infrared information gets mapped to marked points on the celestial sphere. In particular, soft colour-dipole singularities are reproduced to all orders by a correlator of vertex operators in a free-boson theory on the sphere. We then proceed to study soft-gluon currents, and show how bulk results constrain the structure of the celestial theory beyond the free-field limit. For single emission, we note that all logarithms in dipole-like loop contributions can be absorbed into the choice of scale for the strong coupling. For multiple emission, we show how the emerging mixed-helicity celestial operator product expansion must be weighted by energy fractions, breaking holomorphic factorisation and obstructing associativity under successive collinear limits. These results illustrate a remarkable connection between the familiar physics of infrared QCD and the dynamics of a two-dimensional theory on the celestial sphere.