Partially Celestial States and Their Scattering Amplitudes

TL;DR

This paper introduces a new class of representations called 'partially celestial' states in D-dimensional spacetime, generalizing celestial states by incorporating hyperplane-specific transformation properties and constructing associated scattering amplitudes.

Contribution

It develops a framework for partially celestial states with generalized spinor helicity variables, extending celestial amplitudes to hyperplanes of arbitrary dimension in D dimensions.

Findings

Defined generalized spinor helicity variables for all D and p.

Constructed little group covariant amplitudes for partially celestial states.

Explored the application to states with non-local charges.

Abstract

We study representations of the Poincar\'e group that have a privileged transformation law along a p-dimensional hyperplane, and uncover their associated spinor helicity variables in D spacetime dimensions. Our novel representations generalize the recently introduced celestial states and transform as conformal primaries of SO(p,1), the symmetry group of the p-hyperplane. We will refer to our generalized states as ``partially celestial." Following Wigner's method, we find the induced representations, including spin degrees of freedom. Defining generalized spinor helicity variables for every D and p, we are able to construct the little group covariant part of partially celestial amplitudes. Finally, we briefly examine the application of the pairwise little group to partially celestial states with mutually non-local charges.