PIRSA:19120050 Scientific Series Quantum Fields and Strings

DOI10.48660/19120050

Series: Quantum Fields and Strings

Kang, M. (2019). Entanglement wedge reconstruction and operator algebras. Perimeter Institute. https://pirsa.org/19120050

Kang, Monica. Entanglement wedge reconstruction and operator algebras. Perimeter Institute, Dec. 10, 2019, https://pirsa.org/19120050 

@misc{ pirsa_PIRSA:19120050,
  doi = {10.48660/19120050},
  url = {https://pirsa.org/19120050},
  author = {Kang, Monica},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Entanglement wedge reconstruction and operator algebras},
  publisher = {Perimeter Institute},
  year = {2019},
  month = {dec},
  note = {PIRSA:19120050 see, \url{https://pirsa.org}}
}

Abstract

In order to satisfy the Reeh-Schlieder theorem, I study the infinite-dimensional Hilbert spaces using von Neumann algebras. I will first present the theorem that the entanglement wedge reconstruction and the equivalence of relative entropies between the boundary and the bulk (JLMS) are exactly identical. Then I will demonstrate the entanglement wedge reconstruction with a tensor network model of von Neumann algebra with type II1 factor, which guarantees the equivalence between the boundary and the bulk. I will further sketch that this toy model can be generalized to provide more general von Neumann algebras, including the case of a type III1 factor. This can give further insights to understanding quantum gravity from an algebraic perspective.

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