Celestial Holography, A Hitchhiker's Guide to the Celestial Sphere

Abstract

This primer offers an first introduction to Celestial Holography, a rapidly evolving framework aiming to describe quantum gravity in asymptotically flat spacetimes. We start from the established foundation of the AdS/CFT correspondence before venturing into the wilds of Minkowski space. The journey covers the essential Bondi-Sachs formalism and the geometry of null infinity (${\mathcal{I}}^{\pm }$), the discovery of the infinite-dimensional BMS asymptotic symmetry group. We explain the core holographic map given by Mellin transform that recasts four-dimensional scattering amplitudes as correlation functions of a conjectured 2D Celestial Conformal Field Theory (CCFT) on the celestial sphere. The presentation is made intuitive but the mathematics is still precise (hopefully!). It is designed to equip newcomers with both the conceptual landscape and the technical vocabulary to explore this exciting frontier.

30 pages, 7 figures