Primary Fields in Celestial CFT

TL;DR

This work investigates celestial CFT as a holographic framework for 4D scattering by recasting amplitudes as celestial correlators via Mellin transforms. It posits the CCFT energy-momentum tensor T(z) as the shadow of the Δ=0 graviton, a pure-diffeomorphism operator, and analyzes the collinear limits of Einstein–Yang–Mills amplitudes to derive the OPE with gauge-boson operators. The authors show that gauge-boson operators transform as Virasoro primaries under CCFT diffeomorphisms, with conformal weights determined by their Δ and helicity, thereby supporting the emergence of Virasoro symmetry on the celestial sphere. The results solidify a key aspect of CCFT holography and point to further exploration of TT OPE and purely CCFT-based symmetry structures.

Abstract

The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2,C) conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the celestial sphere.