Bulk reconstruction using timelike entanglement in (A)dS

• DOI: 10.48550/arxiv.2312.16056
• Publication Date: 2023-01-01
• Authors: Avijit Das; Shivrat Sachdeva; Debajyoti Sarkar
• Keywords: Anti-de Sitter space; Hamiltonian (control theory)

It is well-known that the entanglement entropies for spacelike subregions, and associated modular Hamiltonians play a crucial role in bulk reconstruction program within Anti de-Sitter (AdS) holography. Explicit examples of HKLL map exist mostly cases where emergent region so-called wedge given boundary subregion. However, motivated from complex pseudo-entropy Euclidean conformal field theories (CFT), one can talk about `timelike entanglement' Lorentzian CFTs dual to AdS spacetimes. One then utilize this timelike define Hamiltonian'. We use constraints involving these manner similar how it was used cases, write down operators regions which are not probed by an RT surface corresponding single CFT. In context two dimensional CFT, we re-derive formulas free scalar fields three examples: Poincar\'{e} patch, inside outside black hole, de Sitter flat slicings. method, no longer requires knowledge dynamics sub-horizon