Partially-massless higher spin algebras in four dimensions

TL;DR

This paper constructs four-dimensional partially-massless higher spin algebras using oscillator methods and Howe duality, revealing their structure and potential deformations for interactions.

Contribution

It provides a novel oscillator-based realization of partially-massless higher spin algebras in four dimensions, connecting them to Howe duality and exploring possible algebra deformations.

Findings

Algebra isomorphism with higher spin spectrum

Oscillator realization via Howe duality

Potential algebra deformations for interactions

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.