Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited
Abstract We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and W 3 higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the reduction gives two copies of chiral bosons on the boundary....
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2023)121 |
| _version_ | 1797675827915128832 |
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| author | Wout Merbis Turmoli Neogi Arash Ranjbar |
| author_facet | Wout Merbis Turmoli Neogi Arash Ranjbar |
| author_sort | Wout Merbis |
| collection | DOAJ |
| description | Abstract We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and W 3 higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the reduction gives two copies of chiral bosons on the boundary. In particular, we take into account the holonomy of the Chern-Simons connection which manifests itself as zero mode of the momentum of the boundary chiral boson. We provide an equivalent formulation of the boundary action which we claim to be the geometric action on symplectic leaves of a (super-)Virasoro or a higher spin W N Poisson manifold in the case of supergravity or higher spin gravity respectively, where the intersection of leaves (given in terms of leaves representatives) can be identified as the bulk holonomy. This concludes the extension to non-linear algebras where the notion of coadjoint representation is not well-defined. The boundary Hamiltonian depends on a choice of boundary conditions and is equivalent to the Schwarzian action for corresponding Brown-Henneaux boundary conditions. We make this connection explicit in the extended supersymmetric case. Moreover, we discuss the geometric action in the case of W 3 AdS3 gravity in both sl $$ \mathfrak{sl} $$ (3) highest weight representations based on principal and diagonal sl $$ \mathfrak{sl} $$ (2) embeddings. |
| first_indexed | 2024-03-11T22:19:17Z |
| format | Article |
| id | doaj.art-d813a8f5ee814ed895689b992159cdd2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T22:19:17Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d813a8f5ee814ed895689b992159cdd22023-09-24T11:07:32ZengSpringerOpenJournal of High Energy Physics1029-84792023-06-012023615010.1007/JHEP06(2023)121Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisitedWout Merbis0Turmoli Neogi1Arash Ranjbar2Dutch Institute for Emergent Phenomena & Institute for Theoretical Physics, University of AmsterdamCentro de Estudios Científicos (CECs)Division of Theoretical Physics, Rudjer Bošković InstituteAbstract We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and W 3 higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the reduction gives two copies of chiral bosons on the boundary. In particular, we take into account the holonomy of the Chern-Simons connection which manifests itself as zero mode of the momentum of the boundary chiral boson. We provide an equivalent formulation of the boundary action which we claim to be the geometric action on symplectic leaves of a (super-)Virasoro or a higher spin W N Poisson manifold in the case of supergravity or higher spin gravity respectively, where the intersection of leaves (given in terms of leaves representatives) can be identified as the bulk holonomy. This concludes the extension to non-linear algebras where the notion of coadjoint representation is not well-defined. The boundary Hamiltonian depends on a choice of boundary conditions and is equivalent to the Schwarzian action for corresponding Brown-Henneaux boundary conditions. We make this connection explicit in the extended supersymmetric case. Moreover, we discuss the geometric action in the case of W 3 AdS3 gravity in both sl $$ \mathfrak{sl} $$ (3) highest weight representations based on principal and diagonal sl $$ \mathfrak{sl} $$ (2) embeddings.https://doi.org/10.1007/JHEP06(2023)121Chern-Simons TheoriesExtended SupersymmetryHigher Spin GravityBlack Holes |
| spellingShingle | Wout Merbis Turmoli Neogi Arash Ranjbar Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited Journal of High Energy Physics Chern-Simons Theories Extended Supersymmetry Higher Spin Gravity Black Holes |
| title | Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited |
| title_full | Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited |
| title_fullStr | Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited |
| title_full_unstemmed | Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited |
| title_short | Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited |
| title_sort | asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited |
| topic | Chern-Simons Theories Extended Supersymmetry Higher Spin Gravity Black Holes |
| url | https://doi.org/10.1007/JHEP06(2023)121 |
| work_keys_str_mv | AT woutmerbis asymptoticdynamicsofthreedimensionalsupergravityandhigherspingravityrevisited AT turmolineogi asymptoticdynamicsofthreedimensionalsupergravityandhigherspingravityrevisited AT arashranjbar asymptoticdynamicsofthreedimensionalsupergravityandhigherspingravityrevisited |