Eikonal amplitudes on the celestial sphere

TL;DR

This paper develops a framework for gravitational celestial amplitudes using eikonal exponentiation, making them analytic with characterized poles and residues, and explores their asymptotic behavior in flat and curved spacetimes.

Contribution

It introduces celestial amplitudes dressed by eikonal phases, providing analytic properties, pole structure, and asymptotic series, advancing the understanding of celestial holography in gravity.

Findings

Celestial amplitudes have poles at negative integer conformal dimensions.

Eikonal dressing yields analytic celestial amplitudes with characterized residues.

Asymptotic series describe large conformal dimension behavior.

Abstract

Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: $2\to2$ scattering of scalars in flat spacetime and $1\to1$ scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, shockwave or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.