Supertranslations call for superrotations

TL;DR

This work surveys the symmetry structure of asymptotically flat spacetimes at null infinity, showing that in higher dimensions the algebra reduces to Poincaré, while in 3D and 4D it expands to infinite-dimensional algebras with supertranslations and superrotations. It analyzes two ways to realize these algebras (asymptotic vs complete gauge fixations), demonstrates their equivalence across gauges, and develops a bulk realization via a metric-dependent bracket tied to Lie algebroids. The paper classifies central extensions of the $rak{bms}_3$ and $rak{bms}_4$ algebras, finding Virasoro-type structures in 3D and Witt-type extensions in 4D, and discusses representation theory and the surface-charge problem. It further outlines future directions, including a field-dependent charge algebra and leveraging 2D CFT tools for 4D gravity, aiming to connect asymptotic symmetries to quantum gravitational observables.

Abstract

We review recent results on symmetries of asymptotically flat spacetimes at null infinity. In higher dimensions, the symmetry algebra realizes the Poincaré algebra. In three and four dimensions, besides the infinitesimal supertranslations that have been known since the sixties, the algebras are evenly balanced because there are also infinitesimal superrotations. We provide the classification of central extensions of the bms3 and bms4 algebras. Applications and consequences as well as directions for future work are briefly indicated.