Celestial superamplitude in $\mathcal N=4$ SYM theory

Celestial amplitude is a new reformulation of momentum space scattering amplitude and offers a promising way for flat holography. In this paper, we study the celestial amplitude in $\mathcal N=4$ Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $\mathcal N=4$ SYM theory. We also compute the three-point and four-point celestial super-amplitude explicitly. They can be identified as the correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $\mathcal N=4$ SYM amplitude via 2D celestial conformal field theory.