BMS4 algebra, its stability and deformations
Abstract We continue analysis of [1] and study rigidity and stability of the b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ algebra and its centrally extended version b m s 4 ^ $$ \widehat{\mathfrak{bm}{\mathfrak{s}}_4} $$ . We construct and classify the family of algebras which appear as de...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2019)068 |
| _version_ | 1811198610968150016 |
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| author | H. R. Safari M. M. Sheikh-Jabbari |
| author_facet | H. R. Safari M. M. Sheikh-Jabbari |
| author_sort | H. R. Safari |
| collection | DOAJ |
| description | Abstract We continue analysis of [1] and study rigidity and stability of the b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ algebra and its centrally extended version b m s 4 ^ $$ \widehat{\mathfrak{bm}{\mathfrak{s}}_4} $$ . We construct and classify the family of algebras which appear as deformations of b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ and in general find the four-parameter family of algebras W $$ \mathcal{W} $$ (a, b; a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) as a result of the stabilization analysis, where b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ = W $$ \mathcal{W} $$ (−1/2, −1/2; −1/2, −1/2). We then study the W $$ \mathcal{W} $$ (a, b; 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 W $$ \mathcal{W} $$ (a, b; a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) family of algebras for generic values of the parameters. For special cases of (a, b) = ( a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) = (0, 0) and (a, b) = (0, −1), ( a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) = (0, 0) the algebra can be deformed. In particular we show that centrally extended W $$ \mathcal{W} $$ (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. |
| first_indexed | 2024-04-12T01:34:14Z |
| format | Article |
| id | doaj.art-a219ec1107d94a80b9bf1f9f58b90fff |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-12T01:34:14Z |
| publishDate | 2019-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a219ec1107d94a80b9bf1f9f58b90fff2022-12-22T03:53:23ZengSpringerOpenJournal of High Energy Physics1029-84792019-04-012019414110.1007/JHEP04(2019)068BMS4 algebra, its stability and deformationsH. R. Safari0M. M. Sheikh-Jabbari1School of Physics, Institute for Research in Fundamental Sciences (IPM)School of Physics, Institute for Research in Fundamental Sciences (IPM)Abstract We continue analysis of [1] and study rigidity and stability of the b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ algebra and its centrally extended version b m s 4 ^ $$ \widehat{\mathfrak{bm}{\mathfrak{s}}_4} $$ . We construct and classify the family of algebras which appear as deformations of b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ and in general find the four-parameter family of algebras W $$ \mathcal{W} $$ (a, b; a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) as a result of the stabilization analysis, where b m s 4 $$ \mathfrak{b}\mathfrak{m}{\mathfrak{s}}_4 $$ = W $$ \mathcal{W} $$ (−1/2, −1/2; −1/2, −1/2). We then study the W $$ \mathcal{W} $$ (a, b; 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 W $$ \mathcal{W} $$ (a, b; a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) family of algebras for generic values of the parameters. For special cases of (a, b) = ( a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) = (0, 0) and (a, b) = (0, −1), ( a ¯ , b ¯ $$ \overline{a},\overline{b} $$ ) = (0, 0) the algebra can be deformed. In particular we show that centrally extended W $$ \mathcal{W} $$ (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.http://link.springer.com/article/10.1007/JHEP04(2019)068Conformal and W SymmetryGauge-gravity correspondenceSpace-Time Symmetries |
| spellingShingle | H. R. Safari M. M. Sheikh-Jabbari BMS4 algebra, its stability and deformations Journal of High Energy Physics Conformal and W Symmetry Gauge-gravity correspondence Space-Time Symmetries |
| title | BMS4 algebra, its stability and deformations |
| title_full | BMS4 algebra, its stability and deformations |
| title_fullStr | BMS4 algebra, its stability and deformations |
| title_full_unstemmed | BMS4 algebra, its stability and deformations |
| title_short | BMS4 algebra, its stability and deformations |
| title_sort | bms4 algebra its stability and deformations |
| topic | Conformal and W Symmetry Gauge-gravity correspondence Space-Time Symmetries |
| url | http://link.springer.com/article/10.1007/JHEP04(2019)068 |
| work_keys_str_mv | AT hrsafari bms4algebraitsstabilityanddeformations AT mmsheikhjabbari bms4algebraitsstabilityanddeformations |