Asymptotic symmetries provide a powerful window into the holographic principle. Unlike pure gauge transformations, they are associated with non-vanishing conserved charges defined at the boundary. However, near infinity the quantities entering these charges typically diverge, rendering a suitable renormalization procedure essential. While holographic renormalization is well understood in asymptotically AdS spacetimes, its flat-space counterpart remains far less developed. In this talk, I will first review the AdS framework and its renormalization program, before surveying the current state of the art in asymptotically flat backgrounds. I will emphasize the central open problems that must be resolved in order to clarify the nature of the putative dual conformal field theory. In particular, I will argue that if such a dual theory exists, whether celestial or Carrollian, it appears to be inherently non-local, which may call into question its physical viability.
Arnaud Delfante (Vienna): Is Flat-Space Holography Renormalizable?
