Subregion Complementarity in AdS/CFT

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Abstract

We examine the bulk reconstruction in the AdS/CFT correspondence. It is believed that CFT operators in a CFT subregion can construct arbitrary bulk local operators in the bulk subregion associated with the CFT subregion. This correspondence is called the entanglement wedge reconstruction or the subregion duality. We argue that the duality fails to hold by presenting problems existing even in a simple setup (the causal wedge reconstruction). Nevertheless, we propose the subregion complementarity, illustrating that different CFT operators can describe a bulk subregion. While we expect that this complementarity is valid outside the horizon in general eternal black holes, it is inapplicable for single-sided black holes where a semi-classical description at the stretched horizon is absent.

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