Soft Limits of Yang-Mills Amplitudes and Conformal Correlators

TL;DR

The paper analyzes tree-level celestial amplitudes in Yang-Mills theory by Mellin transforming plane-wave amplitudes into conformal correlators on the celestial sphere. It shows that the conformally soft limit (Δ→1, λ→0) is governed by low-energy soft emissions, aligning with soft-theorem expectations and derivable from collinear limits. By deriving explicit OPEs for conformal primary gluon operators, it identifies holomorphic and antiholomorphic currents whose Ward identities reproduce the soft constraints in a two-dimensional celestial CFT framework. This work thus forges a direct link between four-dimensional YM soft physics and celestial CFT structure, providing concrete OPE data and CPT-consistent relations to guide future celestial EFT analyses.

Abstract

We study tree-level celestial amplitudes in Yang-Mills theory -- Mellin transforms of multi-gluon scattering amplitudes that convert them into the correlators of conformal primary fields on two-dimensional celestial sphere. By using purely field-theoretical methods, we show that the soft conformal limit of celestial amplitudes, in which one of the primary field operators associated to gauge bosons becomes a dimension one current, is dominated by the contributions of low-energy soft particles. This result confirms conclusions reached by using Yang-Mills theory formulated in curvilinear coordinates, as pioneered by Strominger. By using well-known collinear limits of Yang-Mills amplitudes, we derive the OPE rules for the primary fields and the holomorphic currents arising in the conformally soft limit. The Ward identities following from OPE have the same form as the identities derived by using soft theorems.