BMS Symmetry of Celestial OPE

TL;DR

This paper establishes how BMS symmetry constrains the celestial OPE of two positive-helicity gravitons in four-dimensional Einstein gravity. By performing a Mellin transform of the four-graviton amplitude and studying its holomorphic collinear limit, the authors show that the leading OPE term is fixed by the leading soft theorem, while the first subleading correction is a linear combination of BMS descendants with coefficients determined by BMS algebra. A key result is that, under a suitable notion of BMS primary state, all first-subleading OPE coefficients can be derived from algebraic data, including a non-Poincaré holomorphic supertranslation descendant, and can be organized into Virasoro representations. The work highlights a deep interplay between celestial OPE structure and BMS representation theory, suggesting celestial OPEs may universally assemble into BMS multiplets with descendant coefficients fixed by symmetry. These insights pave the way for a symmetry-driven, non-perturbative handle on celestial correlators and flat-space holography.

Abstract

In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and the coefficient of the leading term in the OPE. This can be done by defining a suitable BMS primary state. We find that among the descendants, which appear at the first subleading order, there is one which is created by holomorphic supertranslation with simple pole on the celestial sphere.