A locality-based commutant argument shows that finite-N holographic CFTs lack the protected logical sector required for holographic quantum error correction, leaving only region-by-region entanglement wedge reconstruction.
Generalized free fields and the AdS-CFT correspondence
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abstract
Motivated by structural issues in the AdS-CFT correspondence, the theory of generalized free fields is reconsidered. A stress-energy tensor for the generalized free field is constructed as a limit of Wightman fields. Although this limit is singular, it fulfils the requirements of a conserved local density for the Poincar'e generators. An explicit "holographic" formula relating the Klein-Gordon field on AdS to generalized free fields on Minkowski space-time is provided, and contrasted with the "algebraic" notion of holography. A simple relation between the singular stress-energy tensor and the canonical AdS stress-energy tensor is exhibited.
fields
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