Celestial Amplitudes: Conformal Partial Waves and Soft Limits

TL;DR

This work develops the celestial amplitudes program by mapping 4D massless scattering to 2D celestial CFT correlators via Mellin transforms and studying CPW decompositions. It presents explicit scalar and gluon four-point CPW decompositions, identifies the full spin content for gluons, and verifies crossing relations and the celestial optical theorem. It derives celestial analogs of single and double soft limits, linking soft theorems to energy-localized celestial correlators. These results advance the holographic understanding of flat spacetime by constraining OPE data, unitarity, and high-energy behavior in celestial CFT.

Abstract

Massless scattering amplitudes in four-dimensional Minkowski spacetime can be Mellin transformed to correlation functions on the celestial sphere at null infinity called celestial amplitudes. We study various properties of massless four-point scalar and gluon celestial amplitudes such as conformal partial wave decomposition, crossing relations and optical theorem. As a byproduct, we derive the analog of the single and double soft limits for all gluon celestial amplitudes.

Figures (1)

• Figure 1: Four-Point Exchange Diagrams