Spinning Boundary Correlators from (A)dS$_4$ Twistors

TL;DR

This work develops a comprehensive twistor-space framework to compute boundary correlators for (A)dS$_4$ via nested Penrose transforms and a boundary limit, reproducing 3d CFT correlators of conserved currents from bulk (anti-)self-dual fields. By translating AdS$_4$ twistors into 3d bispinors on the boundary, the authors obtain compact rational twistor-space representatives and reveal a natural double-copy structure at three points, connecting bulk YM/GR interactions to boundary correlators through a scalar conformal kernel. Regularization is handled through Euclidean signatures for two-point functions and branch-cut constructions for three-point functions, with a Ward-Takahashi identity emerging naturally in this formalism. The framework extends to non-conserved currents (integer $ ext{Δ}$) and to the free scalar, and it clarifies the twistor origin of recent results on cosmological and AdS/CFT correlators, offering a geometric, highly structured route to bulk-boundary correspondences. The results have potential implications for higher-point functions, fermionic extensions, and broader dimensional uplifts via ambitwistor spaces.

Abstract

We develop a twistor-space framework to compute boundary correlators via a boundary limit of nested Penrose transforms in (A)dS$_4$. Starting from correlators of (anti-)self-dual bulk fields, the boundary limit reproduces the correlators of the dual conserved currents; we demonstrate this explicitly for two- and three-point functions. The two-point correlator is rendered finite by working in Euclidean signature. At three points, we obtain compact rational twistor-space representatives obeying a double-copy relation, thereby clarifying the twistor-space origin of the results in Baumann et al. 2024. We further extend the analysis to non-conserved currents with integer conformal dimension, dual to massive bulk fields, as well as to the free scalar.