4d CFT Correlators from Ambitwistors

Abstract

We develop an ambitwistor-space formulation of conserved spinning correlators in four-dimensional CFTs. We show that conformal symmetry and conservation are trivialised by the ambitwistor Penrose transform, and construct the two- and three-point ambitwistor correlators explicitly. We further propose a simple formula for projecting onto parity-even and parity-odd sectors, and verify it in several non-trivial examples. The resulting correlators furnish a natural basis compatible with a boundary double copy for arbitrary spin. At three points, we show that they localise on degree-three curves in a two-twistor representation. We also explain how the formalism incorporates boundary propagators for unitary operators of integer conformal dimension, and extend it to conformally coupled scalars.