Conformally Soft Theorem In Gravity

TL;DR

This work develops celestial amplitudes for gravity by analytic continuation of conformal weights and establishes a conformally soft graviton theorem: in the λ→0 limit, n-point celestial amplitudes factorize into lower-point amplitudes with shifted conformal weights, mirroring Weinberg's soft theorem through the supertranslation Ward identity. The author provides explicit checks for tree-level 4-point amplitudes and heterotic string theory, and argues for a general n-point extension in the MHV sector. The results illuminate how celestial conformal symmetries constrain 4D gravity in a holographic-like basis and clarify UV/IR aspects induced by Mellin transforms. These insights pave the way for a deeper understanding of celestial holography and gravity's infrared structure in a conformal framework.

Abstract

A central feature of scattering amplitudes in gravity or gauge theory is the existence of a variety of energetically soft theorems which put constraints on the amplitudes. Celestial amplitudes which are obtained from momentum-space amplitudes by a Mellin transform over the external particle energies cannot obey the usual energetically soft theorems. Instead, the symmetries of the celestial sphere imply that the scattering of conformally soft particles whose conformal weights under the 4D Lorentz group SL(2,C) are taken to zero obey special relations. Such conformally soft theorems have recently been found for gauge theory. Here, I show conformally soft factorization of celestial amplitudes for gravity and identify it as the celestial analogue of Weinberg's soft graviton theorem.