BRST Noether Theorem and Corner Charge Bracket
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915851368660992 |
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| author | Baulieu, Laurent Wetzstein, Tom Wu, Siye |
| author_facet | Baulieu, Laurent Wetzstein, Tom Wu, Siye |
| contents | We provide a proof of the BRST Noether 1.5th theorem, conjectured in [JHEP 10 (2024) 055], for a broad class of rank-1 BV theories including supergravity and 2-form gauge theories. The theorem asserts that the BRST Noether current of any BRST invariant gauge fixed Lagrangian decomposes on-shell into a sum of a BRST-exact term and a corner term that defines Noether charges. This extends the holographic consequences of Noether's second theorem to gauge fixed theories and, in particular, offers a universal gauge independent Lagrangian derivation of the invariance of the S-matrix under asymptotic symmetries. Furthermore, we show that these corner Noether charges are inherently non-integrable. To address this non-integrability, we introduce a novel charge bracket that accounts for potential symplectic flux and anomalies, providing an honest canonical representation of the asymptotic symmetry algebra. We also highlight a general origin of a BRST cocycle associated with asymptotic symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | BRST Noether Theorem and Corner Charge Bracket Baulieu, Laurent Wetzstein, Tom Wu, Siye High Energy Physics - Theory We provide a proof of the BRST Noether 1.5th theorem, conjectured in [JHEP 10 (2024) 055], for a broad class of rank-1 BV theories including supergravity and 2-form gauge theories. The theorem asserts that the BRST Noether current of any BRST invariant gauge fixed Lagrangian decomposes on-shell into a sum of a BRST-exact term and a corner term that defines Noether charges. This extends the holographic consequences of Noether's second theorem to gauge fixed theories and, in particular, offers a universal gauge independent Lagrangian derivation of the invariance of the S-matrix under asymptotic symmetries. Furthermore, we show that these corner Noether charges are inherently non-integrable. To address this non-integrability, we introduce a novel charge bracket that accounts for potential symplectic flux and anomalies, providing an honest canonical representation of the asymptotic symmetry algebra. We also highlight a general origin of a BRST cocycle associated with asymptotic symmetries. |
| title | BRST Noether Theorem and Corner Charge Bracket |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.17829 |