BMS4 algebra, its stability and deformations

Abstract

Abstract We continue analysis of [1] and study rigidity and stability of the $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ b m s 4 algebra and its centrally extended version $$ \widehat{\mathfrak{bm}{\mathfrak{s}}_4} $$ b m s 4 ^ . We construct and classify the family of algebras which appear as deformations of $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ b m s 4 and in general find the four-parameter family of algebras $$ \mathcal{W} $$ W (a, b; $$ \overline{a},\overline{b} $$ a ¯ , b ¯ ) as a result of the stabilization analysis, where $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ b m s 4 = $$ \mathcal{W} $$ W (−1/2, −1/2; −1/2, −1/2). We then study the $$ \mathcal{W} $$ W (a, b; $$ \overline{a},\overline{b} $$ a ¯ , b ¯ ) algebra, its maximal finite subgroups and stability for different values of the four parameters. We prove stability of the $$ \mathcal{W} $$ W (a, b; $$ \overline{a},\overline{b} $$ a ¯ , b ¯ ) family of algebras for generic values of the parameters. For special cases of (a, b) = ( $$ \overline{a},\overline{b} $$ a ¯ , b ¯ ) = (0, 0) and (a, b) = (0, −1), ( $$ \overline{a},\overline{b} $$ a ¯ , b ¯ ) = (0, 0) the algebra can be deformed. In particular we show that centrally extended $$ \mathcal{W} $$ 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.