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

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.

22 pages, references added, revised version, accepted to JHEP

References in corpus (9)

• Einstein Gravity from Conformal Gravity
• Effective action in a higher-spin background
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• On conformal higher spin wave operators
• Arbitrary spin conformal fields in (A)dS
• Flato-Fronsdal theorem for higher-order singletons
• Global and local properties of AdS(2) higher spin gravity
• Conformal invariant powers of the Laplacian, Fefferman-Graham ambient metric and Ricci gauging
• On manifestly sp(2) invariant formulation of quadratic higher spin Lagrangians

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