Topologically massive higher spin gauge theories

Understand

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.