Partially-massless higher-spin algebras and their finite-dimensional truncations

DOI10.1007/JHEP01(2016)003zbMATH Open1388.83593arXiv1508.07332OpenAlexW1958646696MaRDI QIDQ1638060

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Publication date: 12 June 2018

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Abstract: The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS${}_{d+1}$ are studied. The algebras involving PM generators up to depth $2,(ell-1)$ are defined as the maximal symmetries of free conformal scalar field with $2,ell$ order wave equation in $d$ dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of $(A)d{S}_{d+1}$ isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of $ell-d/2,$, which coincides with the annihilator of the one-row $ell$-box Young diagram representation of $mathfrak{so}_{d+2},$. Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.

Full work available at URL: https://arxiv.org/abs/1508.07332

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