2017/04/30 by Thomas Faulkner, Aitor Lewkowycz · 224 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Computer science #Flow (mathematics) #Geodesic #Geometry #Locality #Mathematical analysis #Mathematics #Modular design #Noncommutative and Quantum Gravity Theories #Operator (biology) #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Wedge (geometry) #hep-th
paper · pdf · doi:10.1007/jhep07(2017)151
published in Journal of High Energy Physics 2017(7) (Springer Nature) · 36 pages, 2 figures
openalex publication_date 2017/07/01 · arxiv created 2018/04/13 · arxiv updated 2018/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We 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.