Celestial amplitudes from UV to IR

A bstract Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV IR physics. We show that known properties quantum gravity translate into powerful constraints on analytic structure celestial amplitudes. For example soft behavior is shown imply exact four-particle amplitude meromorphic complex boost weight plane with poles confined even integers negative real axis. Would-be positive axis from asymptotics be erased by a flat space analog AdS resolution bulk point singularity. The residues identified operator coefficients effective action. Far along axis, argued grow exponentially according black hole area law. Exclusive simply factorize conformally hard factors. factor contains all divergences given current algebra correlator Goldstone bosons spontaneously broken asymptotic symmetries. describes together boost-eigenstate clouds photons or gravitons required These provide an safe $$ \mathcal{S} S -matrix for particles.