# BMS4 Algebra, Its Stability and Deformations

## TL;DR

This paper analyzes the stability and deformations of the BMS4 algebra, classifies a family of related algebras, and explores their physical implications as asymptotic symmetry algebras.

## Contribution

It introduces a four-parameter family of algebras W(a,b;\bar{a},\bar{b}) as deformations of BMS4 and studies their stability and possible deformations.

## Key findings

- W(a,b;\bar{a},\bar{b}) is stable for generic parameters.
- Special parameter choices lead to algebra deformations.
- Deformed algebras include multiple Virasoro subalgebras.

## Abstract

We continue analysis of \cite{Parsa:2018kys} and study rigidity and stability of the BMS4 algebra and its centrally extended version. We construct and classify the family of algebras which appear as deformations of BMS4 and in general find the four-parameter family of algebras W(a,b;\bar{a},\bar{b}) as a result of the stabilization analysis, where BMS4=W(-1/2,-1/2;-1/2,-1/2). We then study the W(a,b;\bar{a},\bar{b}) algebra, its maximal finite subgroups and stability for different values of the four parameters. We prove stability of the W(a,b;\bar{a},\bar{b}) family of algebras for generic values of the parameters. For special cases of (a,b)=(\bar{a},\bar{b})=(0,0) and (a,b)=(0,-1), (\bar{a},\bar{b})=(0,0) the algebra can be deformed. In particular we show that centrally extended W(0,-1;0,0) algebra can be deformed to an algebra which has three copies of Virasoro as a subalgebra. We briefly discuss these deformed algebras as asymptotic symmetry algebras and the physical meaning of the stabilization and implications of our result.