Modified celestial amplitude in Einstein gravity

TL;DR

This work develops a modified Mellin framework for celestial amplitudes by separating asymptotic states in retarded time, introducing a regulator to render tree-level graviton amplitudes finite in Einstein gravity and producing parallel, well-defined expressions for gluons. It demonstrates that these modified amplitudes transform covariantly under Lorentz/Conformal transformations and possess conformal soft factorization, with explicit soft factors and derivative structures in the u-coordinates. The authors compute concrete 4-point graviton and gluon amplitudes, extend soft theorems to the conformal basis, and verify consistency with known soft behavior through 3-point and 4-point analyses in both gravity and Yang–Mills. Overall, the results bolster the interpretation of null infinity data as a 3D conformal theory and advance the program of flat-space holography by providing finite, regulator-compatible celestial amplitudes and their soft limits.

Abstract

In this paper we evaluate the modified celestial amplitude for gravitons and gluons, as defined in arXiv:1801.10171[hep-th]. We find that the modified (tree) amplitude is finite for gravitons in Einstein gravity. The modified amplitude behaves like correlation function of operators inserted at various points of null-infinity in the Minkowski space-time. Therefore, unlike the standard celestial amplitudes, these are three dimensional objects. We also show that this amplitude admits conformal soft factorization recently studied in the literature.