Quite Discrete for a fermion
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916579902488576 |
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| author | Letsios, Vasileios A. Pethybridge, Ben Fukelman, Alan Rios |
| author_facet | Letsios, Vasileios A. Pethybridge, Ben Fukelman, Alan Rios |
| contents | We study Discrete Series representations of $SL(2,\mathbb{R})$ with half-integer scaling dimension $Δ$. At the classical level, we show that these UIRs are realised in the space of mode solutions of spinor fields with imaginary mass parameters on a fixed two-dimensional de Sitter, dS$_{2}$, background. Upon such tuning of the mass, the field develops a fermionic shift symmetry that we characterise. We show that in the Euclidean section this manifests itself in the presence of zero-modes which preclude the definition of a Hadamard two-point function for these UIRs. We propose a Euclidean procedure to deal with the zero-modes, define a two-point function with the right singularity structure, and analyse its late-time behaviour. We end this note by proposing two interacting theories containing the fermionic discrete series in their spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quite Discrete for a fermion Letsios, Vasileios A. Pethybridge, Ben Fukelman, Alan Rios High Energy Physics - Theory We study Discrete Series representations of $SL(2,\mathbb{R})$ with half-integer scaling dimension $Δ$. At the classical level, we show that these UIRs are realised in the space of mode solutions of spinor fields with imaginary mass parameters on a fixed two-dimensional de Sitter, dS$_{2}$, background. Upon such tuning of the mass, the field develops a fermionic shift symmetry that we characterise. We show that in the Euclidean section this manifests itself in the presence of zero-modes which preclude the definition of a Hadamard two-point function for these UIRs. We propose a Euclidean procedure to deal with the zero-modes, define a two-point function with the right singularity structure, and analyse its late-time behaviour. We end this note by proposing two interacting theories containing the fermionic discrete series in their spectrum. |
| title | Quite Discrete for a fermion |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.03724 |