Chern-Simons corner phase space in 4D gravity from BF-BB theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910040094408704 |
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| author | Langenscheidt, Simon |
| author_facet | Langenscheidt, Simon |
| contents | We investigate an approach to determine the correct Poisson brackets of fields restricted to codimension 2 and 3 surfaces in 4D gravity, which are of great potential use in holographic setups and discretisation. Employing a specific BF-BB type parametrisation of gravity which relaxes Plebanski's simplicity constraints, we find that gravity in 4 dimensions carries Chern-Simons like phase spaces in codimension 2 and Kac-Moody algebras in codimension 3. The necessary gauge algebra in this context shows that the appropriate generalisation of the double $\mathcal{D}\mathfrak{so}(1,2)$ of 3D gravity is the Maxwell algebra, $\mathfrak{g}=\mathfrak{so}(1,3)\ltimes(\mathbb{R}^{1,3}\tilde\oplus \mathfrak{so}(1,3)^\ast)$. This realises the corner Poisson bracket of the spin connection for the first time and shows it is off-shell commutative, while the corner metric is noncommutative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03429 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chern-Simons corner phase space in 4D gravity from BF-BB theory Langenscheidt, Simon High Energy Physics - Theory General Relativity and Quantum Cosmology We investigate an approach to determine the correct Poisson brackets of fields restricted to codimension 2 and 3 surfaces in 4D gravity, which are of great potential use in holographic setups and discretisation. Employing a specific BF-BB type parametrisation of gravity which relaxes Plebanski's simplicity constraints, we find that gravity in 4 dimensions carries Chern-Simons like phase spaces in codimension 2 and Kac-Moody algebras in codimension 3. The necessary gauge algebra in this context shows that the appropriate generalisation of the double $\mathcal{D}\mathfrak{so}(1,2)$ of 3D gravity is the Maxwell algebra, $\mathfrak{g}=\mathfrak{so}(1,3)\ltimes(\mathbb{R}^{1,3}\tilde\oplus \mathfrak{so}(1,3)^\ast)$. This realises the corner Poisson bracket of the spin connection for the first time and shows it is off-shell commutative, while the corner metric is noncommutative. |
| title | Chern-Simons corner phase space in 4D gravity from BF-BB theory |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.03429 |