Center-less BMS charge algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914873126944768 |
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| author | Rignon-Bret, Antoine Speziale, Simone |
| author_facet | Rignon-Bret, Antoine Speziale, Simone |
| contents | We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for application to the charge aspects, and introduce a new aspect for Geroch's super-momentum with better covariance properties. For the extended BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas symplectic potential exists, if one is willing to modify the symplectic structure by a corner term. The resulting algebra of Noether currents between two arbitrary cuts is center-less. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and non-radiative. More precisely, super-rotation fluxes act covariantly, but super-rotation charges act covariantly only on global translations. The take home message is that in any situation where 2-cocycles appears in the literature, covariance has likely been lost in the charge prescription, and that the criterium of covariance is a powerful one to reduce ambiguities in the charges, and can be used also for ambiguities in the charge aspects. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_01526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Center-less BMS charge algebra Rignon-Bret, Antoine Speziale, Simone High Energy Physics - Theory General Relativity and Quantum Cosmology We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for application to the charge aspects, and introduce a new aspect for Geroch's super-momentum with better covariance properties. For the extended BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas symplectic potential exists, if one is willing to modify the symplectic structure by a corner term. The resulting algebra of Noether currents between two arbitrary cuts is center-less. The charge algebra at a given cut has a residual field-dependent 2-cocycle, but time-independent and non-radiative. More precisely, super-rotation fluxes act covariantly, but super-rotation charges act covariantly only on global translations. The take home message is that in any situation where 2-cocycles appears in the literature, covariance has likely been lost in the charge prescription, and that the criterium of covariance is a powerful one to reduce ambiguities in the charges, and can be used also for ambiguities in the charge aspects. |
| title | Center-less BMS charge algebra |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.01526 |