Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations

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.