Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations

TL;DR

This work studies the celestial avatar of dual superconformal symmetry in $ ext{N}=4$ Yang-Mills by employing the Mellin transform to relate celestial and momentum-space amplitudes and by deriving the explicit celestial dual generators that annihilate tree-level celestial amplitudes. It derives generalized Banerjee-Ghosh differential equations for color-ordered celestial MHV amplitudes and identifies their momentum-space origin via infinitesimal BCFW shifts, then extends the analysis to supersymmetric cases. It shows that celestial MHV amplitudes are Aomoto-Gelfand hypergeometric functions, whose differential equations arise from momentum conservation and $GL(n-4)$ transformations, and relates these to the BG equations. The results provide a precise bridge between celestial CFT constraints and standard amplitude techniques, offering a structured framework to explore higher helicity sectors and loop effects within celestial holography.

Abstract

Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the Mellin transform. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of $\mathcal{N}=4$ Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial $n$-point tree-level MHV amplitudes and identify their momentum space origins.