Holography in asymptotically flat space-times and the BMS group

TL;DR

This paper argues that holography in asymptotically flat spacetimes can be realized through an S-matrix relating data on past and future null infinity, with the BMS group as the natural boundary symmetry. It develops the link between gravitational infrared sectors and BMS representations, showing that soft graviton states form coherent IR sectors tied to supertranslations and that bulk-boundary matching is subtle and highly dependent on asymptotics. A covariant BMS phase space and a notion of a BMS free Hamiltonian are constructed, highlighting fundamental differences from AdS/CFT and revealing an infinite-dimensional boundary dynamics governed by supertranslations. The work lays groundwork toward a boundary theory on null infinity, while acknowledging that a complete dictionary between bulk and boundary remains challenging and awaiting further development.

Abstract

In a previous paper (hep-th/0306142) we have started to explore the holographic principle in the case of asymptotically flat space-times and analyzed in particular different aspects of the Bondi-Metzner-Sachs (BMS) group, namely the asymptotic symmetry group of any asymptotically flat space-time. We continue this investigation in this paper. Having in mind a S-matrix approach with future and past null infinity playing the role of holographic screens on which the BMS group acts, we connect the IR sectors of the gravitational field with the representation theory of the BMS group. We analyze the (complicated) mapping between bulk and boundary symmetries pointing out differences with respect to the AdS/CFT set up. Finally we construct a BMS phase space and a free hamiltonian for fields transforming w.r.t BMS representations. The last step is supposed to be an explorative investigation of the boundary data living on the degenerate null manifold at infinity.