Bulk locality from modular flow

By T. Faulkner, Aitor Lewkowycz. 2017

211 citations recorded by the source corpus.

A bstractWe study the reconstruction of bulk operators in the entanglement wedge in terms of low energy operators localized in the respective boundary region. To leading order in N, the dual boundary operators are constructed from the modular flow of single trace operators in the boundary subregion. The appearance of modular evolved boundary operators can be understood due to the equality between bulk and boundary modular flows and explicit formulas for bulk operators can be found with a complete understanding of the action of bulk modular flow, a difficult but in principle solvable task.We also obtain an expression when the bulk operator is located on the Ryu-Takayanagi surface which only depends on the bulk to boundary correlator and does not require the explicit use of bulk modular flow. This expression generalizes the geodesic operator/OPE block dictionary to general states and boundary regions.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/46c292cb863f55bb5c1989812476aaaf8e9b6801

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. S. Raju
2. D. Stanford
3. D. Harlow
4. R. Myers
5. J. Maldacena
6. S. Shenker
7. Zhenbin Yang
8. H. Chen

In Statistical and Nonlinear Physics

1. S. Raju
2. D. Stanford
3. D. Harlow
4. R. Myers
5. S. Shenker
6. J. Maldacena
7. H. Chen
8. Ahmed Almheiri

Citations in the corpus

• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “Following [93, 111], the same applies for general time dependent situations.”
• Lessons from the information paradox (2020, background): “) Similarly, the reconstruction of operators in the entanglement wedge as proposed, for instance, in [216] is explicitly state dependent because modular flow is state dependent.”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “Returning to the issue of extracting information from the island, entanglement wedge reconstruction [24, 131–137] allows us to recover information about the island with data from the boundary CFT in the corresponding boundary subregion.”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “The physics in the wedge WA can then be reconstructed from field theory degrees of freedom in A [6–9].”
• Replica wormholes and the black hole interior (2019, background): “This was originally conjectured in [35, 36, 6], and established in [37, 38, 39] using the ideas of [8] A partial exception is [40], but it does not immediately apply to the case of an evaporating black hole.”
• Information radiation in BCFT models of black holes (2019, background): “Further insights in [1–3] make use of the notion of the “entanglement wedge” of a subsystem of a holographic system, which is the portion of the full spacetime that is dual to or reconstructable from the density matrix for the subsystem, and is understood to be the bulk region enclosed by the quantu”