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BMS4 algebra, its stability and deformations

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

Notes

Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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