Flat holography for spinor fields

Abstract

We extend the hyperbolic Milne-slicing construction of flat holography in four-dimensional Minkowski spacetime from scalar fields to massless spin-$\frac{1}{2}$ fields. 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-$\frac{1}{2}$ principal-series primaries. Then we construct regular source-normalized conformal-primary wavefunctions in planar and global coordinates on the celestial sphere $S^2$. We show that the planar source-response kernel is naturally identified with the spin-$\frac{1}{2}$ shadow transform, while inverse shadowing recovers the angular delta-function structure of the unshadowed basis. We also analyze radial renormalization by analytic continuation from the principal-series problem to a real-mass AdS$_3$ problem.