Bulk Locality in AdS/CFT Correspondence

Abstract

In this paper, we study the bulk local states in AdS/CFT correspondence in the large $N$ limit using the formula explicitly relating the bulk local operators and the CFT local operators. We identify the bulk local state in terms of CFT local states and find that the bulk local state corresponds to a CFT state supported in the whole space, which means a version of the subregion duality is not valid. On the other hand, CFT states supported in a space region are expressed in terms of the bulk states supported in a certain region. We find that the quantum error correction proposal is not realized although the puzzles of the radial locality which motivated the proposal are resolved in our analysis. For the understating of the bulk local states, an explicit realization of an analogue of the Reeh-Schlieder theorem plays an important role.

27 pages, v2: minor corrections, references added, v3: minor corrections, references added

References in corpus (8)

• Holography from Conformal Field Theory
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• Constructing local bulk observables in interacting AdS/CFT
• CFT representation of interacting bulk gauge fields in AdS
• Poking Holes in AdS/CFT: Bulk Fields from Boundary States
• Explicit reconstruction of the entanglement wedge
• Holography and unitarity

Cited by in corpus (8)

• Weak Gravity Conjecture from Conformal Field Theory: A Challenge from Hyperscaling Violating and Kerr-Newman-AdS Black Holes
• On the Dynamics in the AdS/BCFT Correspondence
• Rindler Bulk Reconstruction and Subregion Duality in AdS/CFT
• HKLL bulk reconstruction for small $\Delta$
• HKLL for the Non-Normalizable Mode
• Fractional Klein-Gordon Equation on AdS${}_{2+1}$
• Wormholes, geons, and the illusion of the tensor product
• Simple Bulk Reconstruction in AdS/CFT Correspondence