Celestial Superamplitudes
Andreas Brandhuber, Graham R. Brown, Joshua Gowdy, Bill Spence,, Gabriele Travaglini

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 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 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.
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