Topologically massive higher spin gauge theories

Abstract

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- $$ \frac{n}{2} $$ n 2 gauge field $$ {h}_{(n)}={h}_{\alpha_1\dots {\alpha}_n} $$ h n = h α 1 … α 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- $$ \frac{n}{2} $$ n 2 representations of the 3D Poincaré group. Finally, we develop $$ \mathcal{N}=1 $$ N = 1 supersymmetric extensions of the above results.