Celestial Superamplitudes

TL;DR

The paper develops a chiral spinor-helicity framework and a corresponding chiral Mellin transform to define celestial amplitudes with an explicit spin constraint $h-ar{h}=J$. Focusing on $ abla N=4$ SYM, it constructs a consistent on-shell celestial superspace and derives celestial superamplitudes, along with the full celestial superconformal algebra, showing these generators annihilate tree-level amplitudes. It provides concrete three-, four-, and five-point MHV celestial superamplitudes and outlines the general $n$-point structure, with explicit weight assignments for all celestial operators. The approach clarifies how Lorentz and superconformal symmetries act on celestial data, offering a streamlined path toward a 2D celestial SCFT interpretation and promising extensions to gravity, less-supersymmetric theories, and loop-level celestial amplitudes.

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.