  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.
