# BMS4 algebra, its stability and deformations

• H. R. Safari
• M. M. Sheikh-Jabbari
Open Access
Regular Article - Theoretical Physics

## Abstract

We continue analysis of [1] and study rigidity and stability of the $$\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4$$ algebra and its centrally extended version $$\widehat{\mathfrak{bm}{\mathfrak{s}}_4}$$. We construct and classify the family of algebras which appear as deformations of $$\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4$$ and in general find the four-parameter family of algebras $$\mathcal{W}$$(a, b; $$\overline{a},\overline{b}$$) as a result of the stabilization analysis, where $$\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4$$ = $$\mathcal{W}$$(−1/2, −1/2; −1/2, −1/2). We then study the $$\mathcal{W}$$(a, b; $$\overline{a},\overline{b}$$) algebra, its maximal finite subgroups and stability for different values of the four parameters. We prove stability of the $$\mathcal{W}$$(a, b; $$\overline{a},\overline{b}$$) family of algebras for generic values of the parameters. For special cases of (a, b) = ($$\overline{a},\overline{b}$$) = (0, 0) and (a, b) = (0, −1), ($$\overline{a},\overline{b}$$) = (0, 0) the algebra can be deformed. In particular we show that centrally extended $$\mathcal{W}$$(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.

## Keywords

Conformal and W Symmetry Gauge-gravity correspondence Space-Time Symmetries

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