(Non-)unitarity of strictly and partially massless fermions on de Sitter space
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| Format: | Preprint |
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2023
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| _version_ | 1866912765533224960 |
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| author | Letsios, Vasileios A. |
| author_facet | Letsios, Vasileios A. |
| contents | 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 $D=4$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_00420 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | (Non-)unitarity of strictly and partially massless fermions on de Sitter space Letsios, Vasileios A. High Energy Physics - Theory Mathematical Physics 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 $D=4$. |
| title | (Non-)unitarity of strictly and partially massless fermions on de Sitter space |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2303.00420 |