Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
Abstract We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic charges forming an algebra of vector fields. In the case...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2023)154 |
| _version_ | 1797736497437212672 |
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| author | Marc Geiller Florian Girelli Christophe Goeller Panagiotis Tsimiklis |
| author_facet | Marc Geiller Florian Girelli Christophe Goeller Panagiotis Tsimiklis |
| author_sort | Marc Geiller |
| collection | DOAJ |
| description | Abstract We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic charges forming an algebra of vector fields. In the case of 3d BF theory (i.e. 3d gravity), it was shown in [1] that this construction leads to a two-dimensional family of diffeomorphism charges which satisfy a certain modular duality. Here we show that adapting this construction to 4d BF theory first requires to split the underlying gauge algebra. Surprisingly, the space of well-defined quadratic generators can then be shown to be once again two-dimensional. In the case of tangential vector fields, this canonically endows 4d BF theory with a diff(S 2) × diff(S 2) or diff(S 2) ⋉ vect(S 2)ab algebra of boundary symmetries depending on the gauge algebra. The prospect is to then understand how this can be reduced to a gravitational symmetry algebra by imposing Plebański simplicity constraints. |
| first_indexed | 2024-03-12T13:13:39Z |
| format | Article |
| id | doaj.art-a1c782b3c8a242c8af51bb636d91b97e |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:13:39Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a1c782b3c8a242c8af51bb636d91b97e2023-08-27T11:05:57ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023512810.1007/JHEP05(2023)154Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTsMarc Geiller0Florian Girelli1Christophe Goeller2Panagiotis Tsimiklis3Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, UMR 5672Department of Applied Mathematics, University of WaterlooArnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität MünchenDepartment of Applied Mathematics, University of WaterlooAbstract We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic charges forming an algebra of vector fields. In the case of 3d BF theory (i.e. 3d gravity), it was shown in [1] that this construction leads to a two-dimensional family of diffeomorphism charges which satisfy a certain modular duality. Here we show that adapting this construction to 4d BF theory first requires to split the underlying gauge algebra. Surprisingly, the space of well-defined quadratic generators can then be shown to be once again two-dimensional. In the case of tangential vector fields, this canonically endows 4d BF theory with a diff(S 2) × diff(S 2) or diff(S 2) ⋉ vect(S 2)ab algebra of boundary symmetries depending on the gauge algebra. The prospect is to then understand how this can be reduced to a gravitational symmetry algebra by imposing Plebański simplicity constraints.https://doi.org/10.1007/JHEP05(2023)154Gauge SymmetrySpace-Time SymmetriesTopological Field TheoriesGlobal Symmetries |
| spellingShingle | Marc Geiller Florian Girelli Christophe Goeller Panagiotis Tsimiklis Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs Journal of High Energy Physics Gauge Symmetry Space-Time Symmetries Topological Field Theories Global Symmetries |
| title | Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs |
| title_full | Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs |
| title_fullStr | Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs |
| title_full_unstemmed | Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs |
| title_short | Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs |
| title_sort | diffeomorphisms as quadratic charges in 4d bf theory and related tqfts |
| topic | Gauge Symmetry Space-Time Symmetries Topological Field Theories Global Symmetries |
| url | https://doi.org/10.1007/JHEP05(2023)154 |
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