Flat holography for spinor fields

TL;DR

This paper establishes a holographic correspondence for massive spinor fields in flat four-dimensional spacetime, deriving boundary correlators with conformal symmetry and connecting bulk spinor behavior to celestial operators.

Contribution

It develops a flat-space holographic dictionary for spinor fields, reducing the Dirac problem to effective AdS3 problems and clarifying the boundary-to-bulk mapping for spinor operators.

Findings

Derived two-point correlators with conformal symmetry on the celestial sphere.

Reduced 4D Dirac problem to a family of AdS3 problems.

Constructed spinor conformal primary wavefunctions and related them to flat-space bulk-to-boundary maps.

Abstract

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.