Flat holography for spinor fields

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 ${\mathrm{A}\mathrm{d}\mathrm{S}}_3$). 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 ${\mathrm{A}\mathrm{d}\mathrm{S}}_3$ 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.