The Holographic Soft $S$-Matrix in QED and Gravity

TL;DR

This paper demonstrates that leading-order soft S-matrices in QED and gravity can be represented as two-dimensional correlation functions on the celestial sphere, revealing holographic structures and double copy relations.

Contribution

It introduces a holographic framework expressing soft S-matrices in QED and gravity as 2D models, unifying real and virtual divergences.

Findings

Soft S-matrices are fully described by 2D scalar field models.

Soft divergences can be expressed as correlation functions on the celestial sphere.

Holographic and double copy structures emerge in the analysis.

Abstract

At leading order, the $S$-matrices in QED and gravity are known to factorise, providing unambiguous determinations of the parts divergent due to infrared contributions. The soft $S$-matrices defined in this fashion are shown to be defined entirely in terms of $2$ dimensional models on the celestial sphere, involving two real scalar fields, allowing us to express the soft $S$-matrices for real as well as virtual divergences as two dimensional correlation functions. We discuss what this means for finding holographic representations of scattering amplitudes in QED and gravity and comment on simple double copy structures that arise during the analysis.