Shifting Spin on the Celestial Sphere

TL;DR

This paper develops a unified framework for conformal primary wavefunctions across all half-integer spins, revealing their structure, symmetries, and relationships to solutions of Einstein's equations, including black holes and shockwaves.

Contribution

It introduces a new spin frame, identifies key conformal primary wavefunctions, and demonstrates their relation to Einstein solutions via the double copy, extending the understanding of radiative modes and symmetries.

Findings

Conformal primary wavefunctions are systematically organized using a new spin frame.

Massless spin-3/2 conformal primary wavefunction and Goldstone modes are identified.

Conformal primary metrics satisfy the double copy and solve Einstein's equations for Petrov type N.

Abstract

We explore conformal primary wavefunctions for all half integer spins up to the graviton. Half steps are related by supersymmetry, integer steps by the classical double copy. The main results are as follows: we 1) introduce a convenient spin frame and null tetrad to organize all radiative modes of varying spin; 2) identify the massless spin-3/2 conformal primary wavefunction as well as the conformally soft Goldstone mode corresponding to large supersymmetry transformations; 3) indicate how to express a conformal primary of arbitrary spin in terms of differential operators acting on a scalar primary; 4) demonstrate that conformal primary metrics satisfy the double copy in a variety of forms -- operator, Weyl, and Kerr-Schild -- and are exact, albeit complex, solutions to the fully non-linear Einstein equations of Petrov type N; 5) propose a novel generalization of conformal primary wavefunctions; and 6) show that this generalization includes a large class of physically interesting metrics corresponding to ultra-boosted black holes, shockwaves and more.