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

Abstract

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 (dSD) and Unitary Irreducible Representations (UIR’s) of the de Sitter algebra spin(D, 1). Our approach is based on expressing the eigenmodes on global dSD 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 dSD, are not unitary unless D = 4.