Asymptotic symmetries of three dimensional gravity and the membrane paradigm
Abstract The asymptotic symmetry group of three-dimensional (anti) de Sitter space with Brown-Henneaux boundary conditions is the two dimensional conformal group with central charge c = 3ℓ/2G. Usually the asymptotic charge algebra is derived using the symplectic structure of the bulk Einstein equati...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-02-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2019)125 |
| _version_ | 1818325741431947264 |
|---|---|
| author | Mariana Carrillo-González Robert F. Penna |
| author_facet | Mariana Carrillo-González Robert F. Penna |
| author_sort | Mariana Carrillo-González |
| collection | DOAJ |
| description | Abstract The asymptotic symmetry group of three-dimensional (anti) de Sitter space with Brown-Henneaux boundary conditions is the two dimensional conformal group with central charge c = 3ℓ/2G. Usually the asymptotic charge algebra is derived using the symplectic structure of the bulk Einstein equations. Here, we derive the asymptotic charge algebra by a different route. First, we formulate the dynamics of the boundary as a 1+1-dimensional dynamical system. Then we realize the boundary equations of motion as a Hamiltonian system on the dual Lie algebra, g ∗ $$ {\mathfrak{g}}^{\ast } $$ , of the two-dimensional conformal group. Finally, we use the Lie-Poisson bracket on g ∗ $$ {\mathfrak{g}}^{\ast } $$ to compute the asymptotic charge algebra. This streamlines the derivation of the asymptotic charge algebra because the Lie-Poisson bracket on the boundary is significantly simpler than the symplectic structure derived from the bulk Einstein equations. It also clarifies the analogy between the infinite dimensional symmetries of gravity and fluid dynamics. |
| first_indexed | 2024-12-13T11:49:18Z |
| format | Article |
| id | doaj.art-307830a5b0814bdbbfa352599ea4dbcf |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T11:49:18Z |
| publishDate | 2019-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-307830a5b0814bdbbfa352599ea4dbcf2022-12-21T23:47:24ZengSpringerOpenJournal of High Energy Physics1029-84792019-02-012019211610.1007/JHEP02(2019)125Asymptotic symmetries of three dimensional gravity and the membrane paradigmMariana Carrillo-González0Robert F. Penna1Center for Particle Cosmology, Department of Physics and Astronomy, University of PennsylvaniaCenter for Theoretical Physics, Department of Physics, Columbia UniversityAbstract The asymptotic symmetry group of three-dimensional (anti) de Sitter space with Brown-Henneaux boundary conditions is the two dimensional conformal group with central charge c = 3ℓ/2G. Usually the asymptotic charge algebra is derived using the symplectic structure of the bulk Einstein equations. Here, we derive the asymptotic charge algebra by a different route. First, we formulate the dynamics of the boundary as a 1+1-dimensional dynamical system. Then we realize the boundary equations of motion as a Hamiltonian system on the dual Lie algebra, g ∗ $$ {\mathfrak{g}}^{\ast } $$ , of the two-dimensional conformal group. Finally, we use the Lie-Poisson bracket on g ∗ $$ {\mathfrak{g}}^{\ast } $$ to compute the asymptotic charge algebra. This streamlines the derivation of the asymptotic charge algebra because the Lie-Poisson bracket on the boundary is significantly simpler than the symplectic structure derived from the bulk Einstein equations. It also clarifies the analogy between the infinite dimensional symmetries of gravity and fluid dynamics.http://link.springer.com/article/10.1007/JHEP02(2019)125Classical Theories of GravitySpace-Time Symmetries |
| spellingShingle | Mariana Carrillo-González Robert F. Penna Asymptotic symmetries of three dimensional gravity and the membrane paradigm Journal of High Energy Physics Classical Theories of Gravity Space-Time Symmetries |
| title | Asymptotic symmetries of three dimensional gravity and the membrane paradigm |
| title_full | Asymptotic symmetries of three dimensional gravity and the membrane paradigm |
| title_fullStr | Asymptotic symmetries of three dimensional gravity and the membrane paradigm |
| title_full_unstemmed | Asymptotic symmetries of three dimensional gravity and the membrane paradigm |
| title_short | Asymptotic symmetries of three dimensional gravity and the membrane paradigm |
| title_sort | asymptotic symmetries of three dimensional gravity and the membrane paradigm |
| topic | Classical Theories of Gravity Space-Time Symmetries |
| url | http://link.springer.com/article/10.1007/JHEP02(2019)125 |
| work_keys_str_mv | AT marianacarrillogonzalez asymptoticsymmetriesofthreedimensionalgravityandthemembraneparadigm AT robertfpenna asymptoticsymmetriesofthreedimensionalgravityandthemembraneparadigm |