Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
Abstract We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern-Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lor...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-07-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP07(2019)118 |
| _version_ | 1818097257719791616 |
|---|---|
| author | Javier Matulich Stefan Prohazka Jakob Salzer |
| author_facet | Javier Matulich Stefan Prohazka Jakob Salzer |
| author_sort | Javier Matulich |
| collection | DOAJ |
| description | Abstract We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern-Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lorentzian theories. In order to define a nondegenerate bilinear form for each of the theories, we introduce (not necessarily central) extensions of the original kinematical algebras. Using the structure of so-called double extensions, this can be done systematically. For homogeneous spaces that arise as a limit of (anti-)de Sitter spacetime, we show that it is possible to take the limit on the level of the action, after an appropriate extension. We extend our systematic construction of nondegenerate bilinear forms also to all higher-dimensional kinematical algebras. |
| first_indexed | 2024-12-10T23:17:39Z |
| format | Article |
| id | doaj.art-8b219482e2924b63ad4fe7dd7f68a076 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T23:17:39Z |
| publishDate | 2019-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8b219482e2924b63ad4fe7dd7f68a0762022-12-22T01:29:48ZengSpringerOpenJournal of High Energy Physics1029-84792019-07-012019715110.1007/JHEP07(2019)118Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimensionJavier Matulich0Stefan Prohazka1Jakob Salzer2Université Libre de Bruxelles and International Solvay Institutes, Physique Mathématique des Interactions FondamentalesUniversité Libre de Bruxelles and International Solvay Institutes, Physique Mathématique des Interactions FondamentalesDepartament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de BarcelonaAbstract We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern-Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lorentzian theories. In order to define a nondegenerate bilinear form for each of the theories, we introduce (not necessarily central) extensions of the original kinematical algebras. Using the structure of so-called double extensions, this can be done systematically. For homogeneous spaces that arise as a limit of (anti-)de Sitter spacetime, we show that it is possible to take the limit on the level of the action, after an appropriate extension. We extend our systematic construction of nondegenerate bilinear forms also to all higher-dimensional kinematical algebras.http://link.springer.com/article/10.1007/JHEP07(2019)118Chern-Simons TheoriesClassical Theories of GravitySpace-Time Symmetries |
| spellingShingle | Javier Matulich Stefan Prohazka Jakob Salzer Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension Journal of High Energy Physics Chern-Simons Theories Classical Theories of Gravity Space-Time Symmetries |
| title | Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension |
| title_full | Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension |
| title_fullStr | Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension |
| title_full_unstemmed | Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension |
| title_short | Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension |
| title_sort | limits of three dimensional gravity and metric kinematical lie algebras in any dimension |
| topic | Chern-Simons Theories Classical Theories of Gravity Space-Time Symmetries |
| url | http://link.springer.com/article/10.1007/JHEP07(2019)118 |
| work_keys_str_mv | AT javiermatulich limitsofthreedimensionalgravityandmetrickinematicalliealgebrasinanydimension AT stefanprohazka limitsofthreedimensionalgravityandmetrickinematicalliealgebrasinanydimension AT jakobsalzer limitsofthreedimensionalgravityandmetrickinematicalliealgebrasinanydimension |