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arXiv · 2603.06794

Flat holography for spinor fields

Dmitry S. Ageev·Anna S. Bernakevich
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Abstract

We develop an asymptotic-coefficient construction for a free Dirac field in four-dimensional Minkowski spacetime using hyperbolic Milne slicing. We solve the massive mode equation and restrict the boundary source--response analysis to the massless sector. Decomposition into harmonics on three-dimensional hyperbolic space, labeled by a continuous principal-series parameter, yields a separated-point nonlocal kernel up to the action normalization and local contact terms. The kernel has the universal form required by two-dimensional conformal covariance for spin-$\tfrac12$ principal-series primaries. We identify the independent boundary spinor component, retain the two neutrally labeled Milne phases $\tau^{\mp i \nu}$, and construct regular source-normalized wavefunctions with conformal-primary covariance in planar and global representations of the celestial sphere $S^2$. A full CCFT interpretation still requires finite-cutoff renormalization, the complementary barred-response pairing, a global identification of the phase sectors with $\mathcal I^\pm$, and matching to the standard energy-Mellin scattering basis.

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Dmitry S. Ageev, Anna S. Bernakevich. 2026-03-06. Flat holography for spinor fields. https://arxiv.org/abs/2603.06794

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