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Abstract: We consider one of the simplest holographic models: higher-spin gravity in 4 dimensions vs. a free vector model in 3 dimensions. We present a picture in which both the bulk and boundary local descriptions descend from a unified description in twistor space. Higher-spin gravity is closely tied to the Penrose transform, which relates bulk massless fields to twistor functions. We develop a new geometric perspective on the Penrose transform, whereby it becomes a peculiar representation of a CPT reflection. We then identify a boundary version of the transform, relating twistor functions to bilocal operators and sources in the CFT. This allows us to write the partition function in manifestly higher-spin-covariant language, line by line in the Feynman diagrams. The famous ambiguity in the bulk Penrose transform becomes related to the gauge redundancy in the boundary sources.
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