Asymptotic Symmetries from finite boxes

TL;DR

The work shows that asymptotic symmetries of gravity in AdS and flat spacetimes can be recovered from finite spatial regions bounded by Dirichlet walls by analyzing linearized diffeomorphisms that displace the wall. In 3D, these wall-displacing modes reproduce the full AdS3 double-Virasoro algebra and, in the flat limit, the 2+1 BMS algebra, while in higher dimensions the AdS and Poincaré algebras arise from j=1 dipole modes with higher-j modes remaining pure gauge. The approach provides a concrete link between regulated finite-box gravities and the conventional asymptotic symmetry structures, and suggests pathways to a regulated, asymptotically flat phase space together with a soft-graviton perspective on BMS. The results motivate further work to rigorously construct the infinite-volume phase space and to extend the analysis to more general perturbations and matter content.

Abstract

It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.