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.
Highlights
Scattering in four-dimensional asymptotically flat spacetimes obeys an infinite-dimensional symmetry algebra that matches the structure of a two-dimensional conformal field theory (CFT) living on the celestial sphere
Mapping S-matrix elements to celestial CFT correlators is an integral transform of on-shell momenta
The goal of the Celestial Holography program is to push beyond kinematics and gain insight into quantum gravity in the bulk asymptotically flat spacetime from the celestial boundary theory
Summary
Scattering in four-dimensional asymptotically flat spacetimes obeys an infinite-dimensional symmetry algebra that matches the structure of a two-dimensional conformal field theory (CFT) living on the celestial sphere. VI A–VI C, respectively, both verifying that these modes become pure gauge when expected and identifying their Petrov type At this point we have a set of nontrivial background configurations with definite conformal weight and spin on which to consider perturbative scattering. Celebrated as exact solutions when they were discovered in the 1970s and 1980s [33,34,35], these metrics have resurfaced recently in the amplitudes literature
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