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

TL;DR

This work identifies and quantifies the classical central extension of the BMS3 asymptotic symmetry algebra in three dimensions. Using covariant phase space techniques, it shows that the charge algebra for $\mathfrak{bms}_3$ acquires a Virasoro-type central term in the cross-bracket between the diffeomorphism and supertranslation sectors, with $c=3/G$. The authors derive explicit boundary conditions, compute the central extension, and relate the flat-space result to the AdS$_3$ Virasoro structure via a contraction limit. These results illuminate the holographic structure of flat three-dimensional gravity and provide concrete central charges for asymptotic symmetries at null infinity.

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.