Subregion Complementarity in AdS/CFT

TL;DR

This paper investigates the limitations of bulk reconstruction in AdS/CFT, showing that subregion duality and entanglement wedge reconstruction are invalid under certain conditions, and proposes a concept of subregion complementarity.

Contribution

It demonstrates the failure of subregion duality and entanglement wedge reconstruction in AdS/CFT, and introduces subregion complementarity as an alternative framework.

Findings

Subregion duality fails at leading order in large N limit.

Entanglement wedge reconstruction is invalid due to non-perturbative effects.

Subregion complementarity allows different CFT operators to describe a bulk subregion.

Abstract

We examine the bulk reconstruction in the 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 non-perturbative 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. 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.