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

A bstract 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.