Shifting Spin on the Celestial Sphere

TL;DR

The paper advances celestial holography by building a spin-frame formalism to organize conformal primary wavefunctions for spins $s \in \{0,\tfrac{1}{2},1,\tfrac{3}{2},2\}$ up to the graviton, including the spin-$\tfrac{3}{2}$ primary and its large-SUSY Goldstone mode. It demonstrates operator methods to shift spin by half-integer steps using supersymmetry and by integer steps via a classical double copy, and shows a robust Weyl and Kerr-Schild double copy structure for these primaries, yielding exact Petrov type N backgrounds. The work extends to shadow primaries, conformally soft limits, and a generalized class of conformal primaries that include non-radiative/off-shell backgrounds, enabling metrics such as Aichelburg-Sexl, ultra-boosted Kerr gyratons, and Dray-'t Hooft shells to be realized as generalized conformal primaries. By connecting these bulk backgrounds to a celestial CFT framework through double-copy and conformal covariance, the paper lays groundwork for a non-perturbative, background-aware formulation of scattering on the celestial sphere with potential implications for OPEs and modular features. Overall, it provides a versatile toolkit to study bulk physics and holographic structure in asymptotically flat spacetimes, uniting radiative and non-radiative sectors under a common conformal and double-copy banner.

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.

Figures (1)

• Figure 1: Loci of support consistent with conformal covariance. Wavefunctions obeying \ref{['gens']} are naturally written in terms of data on the hyperbolic foliation of Minkowski space, multiplied by a homogeneous function in the distance from the hyperplane $q\cdot X=0$. Wavefunctions with restricted support will have that support on a union of some leaves of the hyperbolic foliation with constant $X^2$, on the hyperplane $q\cdot X=0$, or on an intersection thereof (bold and dashed curves).