Asymptotic Symmetries from finite boxes

TL;DR

This paper demonstrates how to derive asymptotic symmetries of infinite gravitational systems by analyzing finite-box regulated models, providing explicit examples in various dimensions and boundary conditions.

Contribution

It offers a concrete method to extract asymptotic symmetries from finite-box gravity setups, including full Virasoro and BMS algebras in relevant dimensions.

Findings

Asymptotic symmetries can be obtained from finite-box models.

Full Virasoro algebra derived for AdS3 in 2+1 dimensions.

BMS algebra recovered for asymptotically flat space.

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 Poincar\'e 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.