Asymptotic symmetries and celestial CFT

Universal relationships between asymptotic symmetries, QFT soft theorems, and low energy observables have reinvigorated attempts at flat space holography. In this talk, I will review recent advances in the celestial holography proposal, where the 4d S-matrix is reconsidered as a 2d correlator on the celestial sphere at null infinity. In this framework, asymptotic particle states are characterized by the point at which they enter or exit the celestial sphere as well as their SL(2,C) Lorentz quantum numbers: namely their conformal scaling dimension and spin instead of the energy and momentum. I will present a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension.