Subregion Complementarity in anti-de Sitter/Conformal Field Theory

Abstract We examine the bulk reconstruction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We demonstrate that the subregion duality fails to hold, highlighting discrepancies between operators in causal wedge reconstruction and those in global reconstruction at the leading order in the large-N limit. We argue the invalidity of the entanglement wedge reconstruction based on the holographic quantum error correction code, attributing it to nonperturbative finite-N effects or quantum gravity effects due to the trans-Planckian modes near the horizon. Nevertheless, we propose the subregion complementarity, illustrating that different CFT operators can describe a bulk subregion. Although 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 semiclassical description at the stretched horizon is absent.