Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

TL;DR

This paper demonstrates that the symmetry algebra of three-dimensional asymptotically flat spacetimes at null infinity admits a non-trivial classical central extension similar to the Virasoro algebra, linking it to anti-de Sitter cases.

Contribution

It reveals a classical central extension of the asymptotic symmetry algebra in three dimensions, extending the understanding of symmetries at null infinity.

Findings

The symmetry algebra is a semi-direct sum of circle diffeomorphisms and supertranslations.

A non-trivial Virasoro-type central extension exists for the charge algebra.

The central extension closely relates to the anti-de Sitter case.

Abstract

The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of supertranslations. The associated charge algebra is shown to admit a non trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.