Multi-particle Celestial Operator Product Expansions from the Boundary

TL;DR

This paper establishes a detailed correspondence between multi-particle operator product expansions in celestial holography and collinear limits of bulk scattering amplitudes, confirming their consistency across multiple derivation methods.

Contribution

It introduces a comprehensive derivation of multi-particle celestial operator product expansions from conformal field theory, bulk collinear limits, and symmetry principles, unifying these approaches.

Findings

Operator product expansions are determined by single-particle singularities.

Derived expansions match bulk collinear limits in Yang-Mills and gravity.

Coefficients obtained from three independent methods agree precisely.

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.