Conformal Killing Tensors, Noether Currents and Higher-Spin Shift Symmetries in (A)dS Space

For certain mass values, shift symmetries appear among massive higher spin fields propagating on (anti-) de Sitter spacetime. On the one hand, Noether's theorem assigns a set of conserved currents for each shift symmetric field, one current for each of the independent shift symmetries. On the other hand, each shift symmetric field comes with a higher-rank conserved field strength that can be contracted with a conformal Killing tensor (CKT) to form another set of conserved currents, one for each independent CKT. This second set is naively much larger than the first. We conjecture, and prove in the first few cases, that these two sets are the same once we account for the redundancy due to trivial currents that is implicit in Noether's theorem. For each field, only one branch of the CKTs is non-trivial. As we range over all the mass values and spins of the shift symmetric fields, each kind of CKT gets used exactly once in a non-trivial current.