(Non-)unitarity of strictly and partially massless fermions on de Sitter space

We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin s = 3/2, 5/2 with any mass parameter on D-dimensional (D ≥ 3) de Sitter space (dS_D) and Unitary Irreducible Representations (UIR's) of the de Sitter algebra spin(D, 1). Our approach is based on expressing the eigenmodes on global dS_D in terms of eigenmodes of the Dirac operator on the (D - 1)-sphere, which provides a natural way to identify the corresponding representations with known UIR's under the decomposition spin(D, 1) ⊃ spin(D). Remarkably, we find that four- dimensional de Sitter space plays a distinguished role in the case of the gauge-invariant theories. In particular, the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields on dS_D, are not unitary unless D = 4.