Abstract
In this paper, we study the bulk local states in the $\mathrm{AdS}/\mathrm{CFT}$ correspondence in the large $N$ limit using the formula explicitly relating the bulk local operators and the conformal field theory (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 analog of the Reeh-Schlieder theorem plays an important role.
Highlights
AND SUMMARYThe AdS=conformal field theory (CFT) correspondence [1] is highly nontrivial and important in various aspects of physics and has been investigated intensively
The key ingredient of the AdS=CFT correspondence is the locality in the bulk, which is needed for the emergence of the extra dimension
The structure of the quantum error correction codes has not been explicitly identified in realistic models of the AdS=CFT correspondence. It is worth investigating these puzzles in the bulk local states or the bulk local operator expressed by the energy eigenstates of CFTd in the large N limit using the results in [7]
Summary
The AdS=CFT correspondence [1] is highly nontrivial and important in various aspects of physics and has been investigated intensively. The structure of the quantum error correction codes has not been explicitly identified in realistic models of the AdS=CFT correspondence It is worth investigating these puzzles in the bulk local states or the bulk local operator expressed by the energy eigenstates of CFTd in the large N limit using the results in [7]. We find that two bulk local states at a same spacetime point constructed from CFT states supported in space regions A and A0 are different generically if A ≠ A0, even in the low energy theory This means that the quantum error correction code proposal [29] is not realized the puzzles of the radial locality raised in [29] are resolved. We explicitly identify the bulk local state as a CFT state and we identify a CFT state supported in a space region as a bulk state
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