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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2603.06794 |
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| _version_ | 1866915841889533952 |
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| author | Ageev, Dmitry S. Bernakevich, Anna S. |
| author_facet | Ageev, Dmitry S. Bernakevich, Anna S. |
| contents | We develop a flat-space holographic dictionary for a free massive spinor field in four-dimensional Minkowski spacetime, using the hyperbolic (Milne) slicing into $\mathbb H^3$ (Euclidean $\mathrm{AdS}_3$). Decomposing bulk fields into $\mathbb H^3$ harmonics labeled by a continuous parameter, we obtain the renormalized on-shell action as a functional of boundary data and extract the corresponding two-point correlation functions of dual spinning operators on the celestial sphere. The resulting correlators take the universal form dictated by two-dimensional conformal symmetry for spin-$\frac{1}{2}$ primaries. In this way, the four-dimensional Dirac problem is reduced to a family of effective $\mathrm{AdS}_3$ problems, closely following the logic of standard AdS/CFT. We show how the near-boundary behavior of the bulk spinor selects the appropriate celestial sources and determines the conformal dimension of the dual operators. As a further application, we construct the associated spinor conformal primary wavefunctions and clarify their relation to the flat-space bulk-to-boundary map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flat holography for spinor fields Ageev, Dmitry S. Bernakevich, Anna S. High Energy Physics - Theory General Relativity and Quantum Cosmology We develop a flat-space holographic dictionary for a free massive spinor field in four-dimensional Minkowski spacetime, using the hyperbolic (Milne) slicing into $\mathbb H^3$ (Euclidean $\mathrm{AdS}_3$). Decomposing bulk fields into $\mathbb H^3$ harmonics labeled by a continuous parameter, we obtain the renormalized on-shell action as a functional of boundary data and extract the corresponding two-point correlation functions of dual spinning operators on the celestial sphere. The resulting correlators take the universal form dictated by two-dimensional conformal symmetry for spin-$\frac{1}{2}$ primaries. In this way, the four-dimensional Dirac problem is reduced to a family of effective $\mathrm{AdS}_3$ problems, closely following the logic of standard AdS/CFT. We show how the near-boundary behavior of the bulk spinor selects the appropriate celestial sources and determines the conformal dimension of the dual operators. As a further application, we construct the associated spinor conformal primary wavefunctions and clarify their relation to the flat-space bulk-to-boundary map. |
| title | Flat holography for spinor fields |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.06794 |