Celestial Amplitudes from UV to IR

TL;DR

This paper explores how celestial amplitudes encode UV and IR physics in quantum gravity, revealing their analytic structure, pole behavior, and factorization properties, leading to an IR-safe scattering framework.

Contribution

It demonstrates the meromorphic nature of four-particle celestial amplitudes and connects their poles and residues to IR effective action coefficients and asymptotic symmetries.

Findings

Celestial amplitudes are meromorphic with poles on negative even integers.

UV and IR properties constrain the analytic structure of celestial amplitudes.

Factorization into conformally hard and soft parts isolates IR divergences.

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.