Celestial amplitudes and conformal soft theorems

TL;DR

The paper develops a universal framework to express massless tree-level scattering in a celestial conformal basis across dimensions, using CHY and ambitwistor-string formalisms. It derives compact celestial amplitudes and a family of conformal soft theorems for gluons and gravitons, in particular at Δ→1 (gauge/gravity) and Δ→0 (gravity), including four-dimensional refinements. It then reveals how conformally soft vertex operators act as charges generating asymptotic symmetries at null infinity, connecting soft limits to the BMS-like structure on the celestial sphere. Collectively, these results provide a holographic-like perspective on flat-space scattering and illuminate the symmetry structure governing celestial amplitudes.

Abstract

Scattering amplitudes in $d+2$ dimensions can be expressed in terms of a conformal basis, for which the S-matrix behaves as a CFT correlation function on the celestial $d$-sphere. We explain how compact expressions for the full tree-level S-matrix of gauge theory, gravity and other QFTs extend to this conformal basis, and are easily derived from ambitwistor strings. Using these formulae and their worldsheet origins, we prove various tree-level 'conformal soft theorems' in gauge theory and gravity in any dimension; these arise from limits where the scaling dimension of an external state in the scattering process takes special values. These conformally soft limits are obscure from standard methods, but they are easily derived with ambitwistor strings. Additionally, we make an identification between the residues of conformally soft vertex operator insertions in ambitwistor strings and charges generating asymptotic symmetries.