A Holographic Model for Soft Photons and Gravitons in Four Dimensions

TL;DR

This paper develops a two-dimensional holographic model on the celestial sphere to describe infrared phenomena in four-dimensional gauge and gravitational theories, reproducing key theorems and addressing infrared divergences.

Contribution

It introduces a novel holographic framework that captures infrared effects and constructs infrared-finite dressed states in four-dimensional theories.

Findings

Reproduces antipodal matching conditions for Goldstone modes

Derives leading soft photon and graviton theorems

Constructs infrared-finite scattering amplitudes with dressed states

Abstract

We construct a two-dimensional action on the celestial sphere that describes the infrared sector of Abelian gauge and gravitational theories in four dimensions. In particular, we use the holographic model to reproduce (1) antipodal matching conditions for the superphaserotation and supertranslation Goldstone modes in four dimensions, (2) leading soft photon and graviton theorems, and (3) infrared factorization of amplitudes with generic dressed $in$ and $out$ states. Using (3), we reproduce the infrared divergences that plague the standard undressed amplitudes, and show that amplitudes involving Faddeev-Kulish dressed states are infrared finite. As a corollary, we use our holographic model to construct an infinite class of dressed states that give rise to infrared finite scattering amplitudes.