Lorentz-diffeomorphism edge modes in 3d gravity
Abstract The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to restore gauge invariance with respect to gauge transformations supported on the boundary, and on the other hand to p...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2018)029 |
| _version_ | 1819060297315385344 |
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| author | Marc Geiller |
| author_facet | Marc Geiller |
| author_sort | Marc Geiller |
| collection | DOAJ |
| description | Abstract The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to restore gauge invariance with respect to gauge transformations supported on the boundary, and on the other hand to parametrize the largest set of boundary symmetries which can arise if both the gauge parameters and the dynamical fields are unconstrained at the boundary. In this work we construct the extended phase space for three-dimensional gravity in first order connection and triad variables. There, the edge mode fields consist of a choice of coordinate frame on the boundary and a choice of Lorentz frame on the bundle, which together constitute the Lorentz-diffeomorphism edge modes. After constructing the extended symplectic structure and proving its gauge invariance, we study the boundary symmetries and the integrability of their generators. We find that the infinite-dimensional algebra of boundary symmetries with first order variables is the same as that with metric variables, and explain how this can be traced back to the expressions for the diffeomorphism Noether charge in both formulations. This concludes the study of extended phase spaces and edge modes in three-dimensional gravity, which was done previously by the author in the BF and Chern-Simons formulations. |
| first_indexed | 2024-12-21T14:24:45Z |
| format | Article |
| id | doaj.art-09adc1070cca47339ebc529f4c888430 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T14:24:45Z |
| publishDate | 2018-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-09adc1070cca47339ebc529f4c8884302022-12-21T19:00:40ZengSpringerOpenJournal of High Energy Physics1029-84792018-02-012018212810.1007/JHEP02(2018)029Lorentz-diffeomorphism edge modes in 3d gravityMarc Geiller0Perimeter Institute for Theoretical PhysicsAbstract The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to restore gauge invariance with respect to gauge transformations supported on the boundary, and on the other hand to parametrize the largest set of boundary symmetries which can arise if both the gauge parameters and the dynamical fields are unconstrained at the boundary. In this work we construct the extended phase space for three-dimensional gravity in first order connection and triad variables. There, the edge mode fields consist of a choice of coordinate frame on the boundary and a choice of Lorentz frame on the bundle, which together constitute the Lorentz-diffeomorphism edge modes. After constructing the extended symplectic structure and proving its gauge invariance, we study the boundary symmetries and the integrability of their generators. We find that the infinite-dimensional algebra of boundary symmetries with first order variables is the same as that with metric variables, and explain how this can be traced back to the expressions for the diffeomorphism Noether charge in both formulations. This concludes the study of extended phase spaces and edge modes in three-dimensional gravity, which was done previously by the author in the BF and Chern-Simons formulations.http://link.springer.com/article/10.1007/JHEP02(2018)029Classical Theories of GravityGauge SymmetryGlobal Symmetries |
| spellingShingle | Marc Geiller Lorentz-diffeomorphism edge modes in 3d gravity Journal of High Energy Physics Classical Theories of Gravity Gauge Symmetry Global Symmetries |
| title | Lorentz-diffeomorphism edge modes in 3d gravity |
| title_full | Lorentz-diffeomorphism edge modes in 3d gravity |
| title_fullStr | Lorentz-diffeomorphism edge modes in 3d gravity |
| title_full_unstemmed | Lorentz-diffeomorphism edge modes in 3d gravity |
| title_short | Lorentz-diffeomorphism edge modes in 3d gravity |
| title_sort | lorentz diffeomorphism edge modes in 3d gravity |
| topic | Classical Theories of Gravity Gauge Symmetry Global Symmetries |
| url | http://link.springer.com/article/10.1007/JHEP02(2018)029 |
| work_keys_str_mv | AT marcgeiller lorentzdiffeomorphismedgemodesin3dgravity |