Multi-particle Celestial Operator Product Expansions from the Boundary

TL;DR

This work establishes that multi-particle celestial operator product expansions (OPEs) in the boundary CFT dual to 4D asymptotically flat spacetimes are completely determined by the single-particle OPE data. It provides three independent derivations—boundary-boundary Wick-type manipulations using a generalized Wick theorem, bulk collinear-limit analyses of tree-level Yang–Mills and Einstein gravity, and a symmetry-based approach enforcing 4D Poincaré invariance on the boundary—showing precise agreement across all methods. The authors derive explicit holomorphic and full OPEs for general helicities, express multi-particle coefficients in terms of single-particle gamma and beta functions tied to bulk three-point couplings, and demonstrate that multi-particle operators are composite rather than new primaries. These results reduce the independent data required in celestial holography, reinforce the consistency between bulk and boundary pictures, and provide a foundation for exploring loop corrections and the underlying symmetry algebras in celestial CFTs.

Abstract

In celestial holography, scattering particles in four-dimensional asymptotically flat spacetimes are dual to conformal primary field operators on the celestial sphere. Multi-particle celestial operators can be formed from regularized coincident limits of single-particle celestial operators. The singular terms in the operator product expansion of multi-particle operators are shown to be determined entirely by the singular terms in the operator product expansion between single-particle celestial operators, as expected in a standard conformal field theory. Boundary operator product expansions in celestial holography are known to be dual to subtle collinear limits of bulk scattering amplitudes. The multi-particle operator product expansions derived from standard conformal-field theoretic techniques are shown to reproduce precisely the results from the corresponding bulk collinear limits in tree-level Yang-Mills and Einstein gravity. Finally, the coefficients of multi-particle celestial operator product expansions are derived from a third complementary method that enforces bulk four-dimensional translational invariance as a global symmetry of the celestial dual. The results of all three methods agree precisely.