Bulk reconstruction using timelike entanglement in (A)dS
| Autor: | Das, Avijit, Sachdeva, Shivrat, Sarkar, Debajyoti |
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| Rok vydání: | 2023 |
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| Zdroj: | Phys. Rev. D 109, 066007 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.109.066007 |
| Popis: | It is well-known that the entanglement entropies for spacelike subregions, and the associated modular Hamiltonians play a crucial role in the bulk reconstruction program within Anti de-Sitter (AdS) holography. Explicit examples of HKLL map exist mostly for the cases where the emergent bulk region is the so-called entanglement wedge of the given boundary subregion. However, motivated from the complex pseudo-entropy in Euclidean conformal field theories (CFT), one can talk about a `timelike entanglement' in Lorentzian CFTs dual to AdS spacetimes. One can then utilize this boundary timelike entanglement to define a boundary `timelike modular Hamiltonian'. We use constraints involving these Hamiltonians in a manner similar to how it was used for spacelike cases, and write down bulk operators in regions which are not probed by an RT surface corresponding to a single CFT. In the context of two dimensional CFT, we re-derive the HKLL formulas for free bulk scalar fields in three examples: in AdS Poincar\'{e} patch, inside and outside of the AdS black hole, and for de Sitter flat slicings. In this method, one no longer requires the knowledge of bulk dynamics for sub-horizon holography. Comment: Version 2. 51 pages, 13 figures. Minor modifications and corrections. References added. Version 3. Minor changes in abstract and elsewhere. Published version |
| Databáze: | arXiv |
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