Higher-spin algebras from soft theorems I: the wedge condition

TL;DR

This paper constructs a map from celestial sphere functions to differential operators using soft graviton theorems, revealing the wedge subalgebras as natural representation domains for Yang-Mills and gravity.

Contribution

It provides an explicit closed-form formula for the map and identifies wedge subalgebras as the natural domain for representations.

Findings

Explicit formula for the map from functions to differential operators.

Wedge subalgebras form the natural domain for the representation.

Connection between soft theorems and higher-spin algebra structures.

Abstract

In this article we use the sub$^n$-soft graviton theorems to construct the map $\Top$ from the spin-graded set of holomorphic functions on local celestial sphere patches to differential operators acting on the asymptotic data for massless particles at $\scrip$, in analogy with previous results in the literature for the sub$^n$-soft photon theorems. The result is an explicit closed-form formula. We show that the wedge subalgebras for both Yang-Mills and gravity are the natural domain on which $\Top$ becomes a representation.