Celestial Superamplitudes

TL;DR

This paper develops a new framework for celestial amplitudes in (super) Yang-Mills theory using a novel parameterization of spinor helicity variables, leading to natural derivations of conformal constraints and superconformal symmetry actions.

Contribution

It introduces a parameterization where the phase of spinor helicity variables is unfixed, deriving the spin constraint and superconformal generators directly from this approach.

Findings

Derivation of the spin constraint $h-ar{h}=J$ from a new Mellin transform.

Representation of superconformal algebra generators acting on celestial amplitudes.

Formulation of chiral celestial superamplitudes in $ =4$ super Yang-Mills.

Abstract

We study celestial amplitudes in (super) Yang-Mills theory using a parameterisation of the spinor helicity variables where their overall phase is not fixed by the little group action. In this approach the spin constraint $h-\bar{h}=J$ for celestial conformal primaries emerges naturally from a new Mellin transform, and the action of conformal transformations on celestial amplitudes is derived. Applying this approach to $\mathcal{N}\!=\!4$ super Yang-Mills, we show how the appropriate definition of on-shell superspace coordinates leads naturally to a formulation of chiral celestial superamplitudes and a representation of the generators of the four-dimensional superconformal algebra on the celestial sphere, which by construction annihilate all tree-level celestial superamplitudes.