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

## TL;DR

This paper investigates the unitarity properties of massless and partially massless fermionic fields of spins 3/2 and 5/2 on de Sitter space, revealing that non-unitarity generally occurs except in four dimensions.

## Contribution

It establishes a detailed correspondence between fermionic field modes on de Sitter space and de Sitter algebra representations, highlighting the special role of four dimensions for unitarity.

## Key findings

- Strictly massless spin-3/2 and spin-5/2 fields are non-unitary in dimensions other than four.
- Partially massless fermions are non-unitary in all dimensions except four.
- Four-dimensional de Sitter space uniquely admits unitary gauge-invariant fermionic fields.

## 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 ($D \geq 3$) 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$(D,1)$ $\supset$ 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 $D=4$.