A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix

TL;DR

This paper refines the understanding of boundary correlators in massless flat spacetime scattering by incorporating soft contributions, revealing new non-distributional effects and linking to celestial amplitude frameworks.

Contribution

It introduces a consistent regulation method for the extrapolate dictionary, including soft components, and connects electric and magnetic Carrollian correlators to celestial data analysis.

Findings

Identification of a soft contribution typically omitted in saddle point approximation.

Boundary correlators include non-distributional contributions on the celestial sphere.

Magnetic branch correlators can be used to extract celestial data from low point correlators.

Abstract

We revisit the extrapolate dictionary for massless scattering in flat spacetime and identify a soft contribution that is typically dropped from the saddle point approximation. We show how to consistently regulate the extrapolation to include both the soft and hard components and identify the boundary correlation functions as a combination of electric and magnetic branch Carrollian correlators. This implies in particular that there are contributions to these boundary correlators that are non-distributional on the celestial sphere. Finally, we close by exploring the utility of the magnetic branch for extracting celestial data from low point correlators: connecting our results to recent work on flat space extrapolate dictionaries and celestial shadow amplitudes.