Bulk Locality in AdS/CFT Correspondence

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.