New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912127399231488 |
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| author | Letsios, Vasileios A. |
| author_facet | Letsios, Vasileios A. |
| contents | We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s \geq 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($dS_{4}$). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of $dS_{4}$, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra $so(4,2)$ up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of $γ^{5}$ times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities $\pm s$ of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra $so(4,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01702 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space Letsios, Vasileios A. High Energy Physics - Theory We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s \geq 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($dS_{4}$). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of $dS_{4}$, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra $so(4,2)$ up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of $γ^{5}$ times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities $\pm s$ of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra $so(4,1)$. |
| title | New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.01702 |