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I wouldn't say that "holographic theories are non-local by definition". On the contrary, in AdS/CFT the CFT is completely local and satisfies cluster decomposition. The cluster decomposition property in AdS can be proved using the CFT bootstrap for all CFTs in $d > 2$ (see http://arxiv.org/abs/arXiv:1212.3616, the proof only requires CFT `axioms', ...



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