The holographic dual of the Penrose transform

TL;DR

This paper develops a holographic duality framework linking twistor functions and CFT operators in higher-spin gravity, providing a twistorial partition function that captures bulk interactions and makes higher-spin symmetry explicit.

Contribution

It introduces a holographic dual to the Penrose transform using twistors, unifying bulk and boundary descriptions and including bulk interactions in the partition function.

Findings

Twistor space offers a nonlocal, gauge-invariant description of the duality.

The twistorial partition function makes higher-spin symmetry manifest.

Bulk interactions are incorporated into the boundary-based partition function.

Abstract

We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these "square root" spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a "square root" of CPT.