(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 ($D\ge 3$) de Sitter space ($d{S}_D$) and Unitary Irreducible Representations (UIR's) of the de Sitter algebra spin$(D,1)$. Our approach is based on expressing the eigenmodes on global $d{S}_D$ 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 $d{S}_D$, are not unitary unless $D=4$.

33 pages (including references), no figures

References in corpus (1)

• The de Sitter group and its presence at the late-time boundary

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