On loop celestial amplitudes for gauge theory and gravity

TL;DR

The paper develops explicit loop-level celestial amplitudes for massless gauge theory and gravity, focusing on finite rational all-plus and single-minus helicity configurations. It uses the celestial (conformal) basis obtained via Mellin transforms of momentum-space amplitudes and provides concrete four- and five-point examples, along with a general prescription for higher points. A key contribution is the explicit all-plus one-loop gluon amplitude integrand and its gravity counterpart, plus a systematic framework (including a generalized Cramer's rule) to obtain higher-point celestial expressions. The work advances the program of flat-space holography by offering tangible loop-level celestial data and highlighting structural parallels with conformal field theories on the celestial sphere.

Abstract

Scattering amplitudes of massless particles in Minkowski space can be expressed in a conformal basis by Mellin transforming the momentum space amplitudes to correlation functions on the celestial sphere at null infinity. In this paper, we study celestial amplitudes of loop level gluons and gravitons. We focus on the rational amplitudes that carry all-plus and single-minus external helicities. Because these amplitudes are finite, they provide a concrete example of celestial amplitudes of Yang- Mills and gravity theory beyond tree level. We give explicit examples of four and five point functions and comment on higher point amplitudes.