# Celestial amplitudes and conformal soft theorems

## TL;DR

This paper presents a conformal basis approach to celestial amplitudes, deriving full tree-level S-matrices for gauge theory and gravity, and establishing conformal soft theorems and their relation to asymptotic symmetries.

## Contribution

It extends the conformal basis for scattering amplitudes, derives compact formulas from ambitwistor strings, and proves conformal soft theorems in any dimension.

## Key findings

- Derived full tree-level S-matrices in conformal basis
- Proved conformal soft theorems for gauge theory and gravity
- Linked residues of soft vertex operators to asymptotic symmetries

## Abstract

Scattering amplitudes in $d+2$ dimensions can be expressed in terms of a conformal basis, for which the S-matrix behaves as a CFT correlation function on the celestial $d$-sphere. We explain how compact expressions for the full tree-level S-matrix of gauge theory, gravity and other QFTs extend to this conformal basis, and are easily derived from ambitwistor strings. Using these formulae and their worldsheet origins, we prove various tree-level 'conformal soft theorems' in gauge theory and gravity in any dimension; these arise from limits where the scaling dimension of an external state in the scattering process takes special values. These conformally soft limits are obscure from standard methods, but they are easily derived with ambitwistor strings. Additionally, we make an identification between the residues of conformally soft vertex operator insertions in ambitwistor strings and charges generating asymptotic symmetries.