(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 $D=4$.

arXiv comment33 pages (including references), no figures

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Cited by in corpus (9)

• The Källén-Lehmann representation in de Sitter spacetime
• de Sitter at all loops: the story of the Schwinger model
• dS${}_2$ Supergravity
• (Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes
• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
• Fermionic Shift Symmetries in (Anti) de Sitter Space
• Partially massless spin 2 and supersymmetry
• Cubic interactions for massless and partially massless spin-1 and spin-2 fields
• Unconventional conformal invariance of maximal depth partially massless fields on $d{S}_4$ and its relation to complex partially massless SUSY