Flat holography for spinor fields

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-$\frac{1}{2}$ 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.

v2: 50 pages, some calculations clarified, references added