BMS Flux Algebra in Celestial Holography

TL;DR

The paper develops a BMS flux algebra for radiative four-dimensional asymptotically flat spacetimes and embeds non-local BMS momentum fluxes into the celestial CFT framework. By splitting fluxes into soft and hard parts, it connects the soft flux to the supertranslation operator and shows the CCFT stress tensor arises from the soft part of the super angular momentum flux, deriving transformation laws and OPEs from the bulk algebra. The work demonstrates that the flux algebra yields CCFT Ward identities and confirms P and T as Virasoro primary and stress-tensor currents in the soft sector, even with superrotations encoded by memory fields. It discusses implications for CCFT constraints, the vanishing of a bulk central charge, and extensions to generalized and Weyl BMS, outlining directions for refining the holographic dictionary and exploring shadow transformations.

Abstract

Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.