Holographic Scattering Amplitudes

Inspired by ancient astronomy, we propose a holographic description of perturbative scattering amplitudes, as integrals over a `celestial sphere'. Since Lorentz invariance, local interactions, and particle propagations all take place in a four-dimensional space-time, it is not trivial to accommodate them in a lower-dimensional `celestial sphere'. The details of this task will be discussed step by step, resulting in the Cachazo-He-Yuan (CHY) and similar scattering amplitudes, thereby providing them with a holographic non-string interpretation.