Local Shadow Celestial Operator Product Expansions

In four-dimensional (4D) asymptotically flat spacetime, the isomorphism SO(3,1) ≅ SL(2,ℂ) underlies an effort to realise a duality with a two-dimensional (2D) conformal field theory (CFT), a flat-space analog of the AdS/CFT correspondence. In this framework, solutions of the 4D linearised massless wave equation are organised into two highest-weight families under 2D SL(2, ℂ) that are related through a shadow transformation. The first is built by Mellin-transforming standard momentum eigenstates to yield so-called celestial primaries whose operator product expansion (OPE) directly encodes the collinear limits of momentum space amplitudes, giving rise to a local 2D OPE structure similar to conventional CFT correlators. The second "shadow" family is a priori non-local and does not have a standard notion of local OPE. We release this tension by providing a general prescription that endows shadow operators with a local OPE. In particular, we provide a study of how OPE coefficients of collinear limits transform under a shadow map for arbitrary n-point functions using OPE blocks, and discuss applications to U(1) currents and stress tensors. Further work includes discussing how this construction relates to analytic continuation from (3,1) to (2,2) signature.