Topologically massive higher spin gauge theories

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 $(2-n\mathrm{/}2)$ and argue that it possesses a Weyl primary descendant $C_{(n)}$ of dimension $(1+n\mathrm{/}2)$. 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 Poincar'e group. Finally, we develop $\mathcal{N}=1$ supersymmetric extensions of the above results.