Topologically massive higher spin gauge theories

Abstract

We elaborate on conformal higher-spin gauge theory in three-dimensional (3D) curved space. For any integer $n>2$ we introduce a conformal spin-$\frac{n}{2}$ gauge field $h_{(n)}=h_{{\alpha }_1\dots {\alpha }_n}$ (with $n$ spinor indices) of dimension $(2-n/2)$ and argue that it possesses a Weyl primary descendant $C_{(n)}$ of dimension $(1+n/2)$. The latter proves to be divergenceless and gauge invariant in any conformally flat space. Primary fields $C_{(3)}$ and $C_{(4)}$ coincide with the linearised Cottino and Cotton tensors, respectively. Associated with $C_{(n)}$ is a Chern-Simons-type action that is both Weyl and gauge invariant in any conformally flat space. These actions, which for $n=3$ and $n=4$ coincide with the linearised actions for conformal gravitino and conformal gravity, respectively, are used to construct gauge-invariant models for massive higher-spin fields in Minkowski and anti-de Sitter space. In the former case, the higher-derivative equations of motion are shown to be equivalent to those first-order equations which describe the irreducible unitary massive spin-$\frac{n}{2}$ representations of the 3D Poincaré group. Finally, we develop $\mathcal{N}=1$ supersymmetric extensions of the above results.

50 pages; V2: typos corrected, comments, references and new appendix added; V3: published version

References in corpus (8)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Reducible higher-spin multiplets in flat and AdS spaces and their geometric frame-like formulation
• Off-shell massive N=1 supermultiplets in three dimensions
• Three-dimensional (p,q) AdS superspaces and matter couplings
• Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS_3 space
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• Minimal $\mathcal{N}=4$ topologically massive supergravity

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