Shifting spin on the celestial sphere

We explore conformal primary wave functions 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- conformal primary wave function 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 nonlinear Einstein equations of Petrov type ; 5) propose a novel generalization of conformal primary wave functions; and 6) show that this generalization includes a large class of physically interesting metrics corresponding to ultra-boosted black holes, shockwaves and more.