On Rigidity of 3d Asymptotic Symmetry Algebras

TL;DR

This paper investigates the rigidity and stability of infinite-dimensional asymptotic symmetry algebras in three-dimensional spacetimes, classifying their deformations and identifying the Virasoro algebra as a key rigid structure.

Contribution

It provides a classification of deformations of BMS3, u(1) Kac-Moody, and Virasoro algebras, revealing the Virasoro algebra's unique rigidity among these.

Findings

Virasoro algebra is a rigid member of the deformation family.

Deformations of BMS3 and u(1) Kac-Moody algebras are classified.

Stabilization of Virasoro is inverse to Inönü-Wigner contraction.

Abstract

We study rigidity and stability of infinite dimensional algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider algebras appearing as asymptotic symmetries of three dimensional spacetimes, the BMS3, u(1) Kac-Moody and Virasoro algebras. We construct and classify the family of algebras which appear as deformations of BMS3, u(1) Kac-Moody and their central extensions by direct computations and also by cohomological analysis. The Virasoro algebra appears as a specific member in this family of rigid algebras; for this case stabilization procedure is inverse of the In\"on\"u-Wigner contraction relating Virasoro to BMS3 algebra. We comment on the physical meaning of deformation and stabilization of these algebras and relevance of the family of rigid algebras we obtain