Higher-spin Cotton tensors and massive gauge-invariant actions in AdS3

A bstract In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor ℭ α ( n ) ( h ) is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential h α ( n ) . The explicit form of ℭ α ( n ) ( h ) is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for ℭ α ( n ) ( h ) in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action S CS n h ∝ ∫ d 3 xeh α n ℭ α n h factorises into a product of ( n − 1) first-order operators that are associated with the spin- n/ 2 partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS 3 . The main results are extended to the case of N = 1 AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS 3 .