Partially-massless higher spin algebras in four dimensions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913433254887424 |
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| author | Basile, Thomas Dhasmana, Shailesh |
| author_facet | Basile, Thomas Dhasmana, Shailesh |
| contents | We propose a realisation of partially-massless higher spin algebras in four dimensions in terms of bosonic and fermionic oscillators, using Howe duality between $sp(4,\mathbb R) \cong so(2,3)$ and $osp(1|2(\ell-1), \mathbb R)$. More precisely, we show that the centraliser of $osp(1|2(\ell-1),\mathbb R)$ in the Weyl--Clifford algebra generated by $4$ bosonic and $8(\ell-1)$ fermionic symbols, modulo $osp(1|2(\ell-1),\mathbb R)$ generators, is isomorphic to the higher spin algebra of the type-A$_\ell$ theory whose spectrum contains partially-massless fields of all spins and depths $t=1,3,\dots,2\ell-1$. We also discuss the possible existence of a deformation of this algebra, which would encode interaction for the type-A$_\ell$ theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partially-massless higher spin algebras in four dimensions Basile, Thomas Dhasmana, Shailesh High Energy Physics - Theory We propose a realisation of partially-massless higher spin algebras in four dimensions in terms of bosonic and fermionic oscillators, using Howe duality between $sp(4,\mathbb R) \cong so(2,3)$ and $osp(1|2(\ell-1), \mathbb R)$. More precisely, we show that the centraliser of $osp(1|2(\ell-1),\mathbb R)$ in the Weyl--Clifford algebra generated by $4$ bosonic and $8(\ell-1)$ fermionic symbols, modulo $osp(1|2(\ell-1),\mathbb R)$ generators, is isomorphic to the higher spin algebra of the type-A$_\ell$ theory whose spectrum contains partially-massless fields of all spins and depths $t=1,3,\dots,2\ell-1$. We also discuss the possible existence of a deformation of this algebra, which would encode interaction for the type-A$_\ell$ theory. |
| title | Partially-massless higher spin algebras in four dimensions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.11884 |