BMS4 Algebra, Its Stability and Deformations

TL;DR

This work extends the deformation analysis of asymptotic symmetry algebras from 3d to 4d by examining the rigidity of the BMS4 algebra and its centrally extended version. It shows that infinitesimal deformations of ${\mathfrak{bms}}_4$ generate a four-parameter family ${\cal W}(a,b;\bar a,\bar b)$, and proves that this family is generically rigid, with special parameter choices admitting additional deformations or larger global subalgebras. Central extensions are incorporated, and a comprehensive cohomological treatment via Hochschild-Serre supports the deformation results, identifying precisely where nontrivial central terms can arise. The analysis reveals that there is no infinite-dimensional algebra in this deformation orbit that contracts to $\mathfrak{so}(3,2)$, contrasting with the 3d case and bearing implications for holography and asymptotic symmetry interpretations on 4d flat spacetimes. Special points in parameter space (e.g., ${\cal W}(0,0;0,0)$ and ${\cal W}(0,-1;0,0)$) exhibit richer structures, such as multiple Virasoro subalgebras, highlighting potential connections to AdS3 physics and related symmetry algebras.

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.