Celestial Amplitudes from UV to IR

TL;DR

The paper develops a celestial-amplitude framework where 4D scattering is expressed in boost eigenstates on the celestial sphere, revealing deep links between UV completion and IR structure. It establishes that, in this basis, UV physics imprints meromorphic structures in the beta plane, with gravity eliminating positive-beta poles and UV data encoded in negative-beta residues and their positivity properties. The IR sector exhibits universal soft factors encoded by Goldstone bosons of spontaneously broken asymptotic symmetries, enabling an IR-safe S-matrix via conformal dressings that factorize into soft and hard parts. Collectively, these results illuminate how UV/IR physics interplays shape celestial amplitudes and point toward a consistent flat-space holographic description anchored by soft theorems and dressings.

Abstract

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