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arXiv · 2407.11884

Partially-massless higher spin algebras in four dimensions

Thomas Basile·Shailesh Dhasmana
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Abstract

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.

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Thomas Basile, Shailesh Dhasmana. 2024-07-16. Partially-massless higher spin algebras in four dimensions. https://arxiv.org/abs/2407.11884

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