Fun with replicas: tripartitions in tensor networks and gravity

Geoff Penington, Michael Walter, Freek Witteveen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

4 Citations (Scopus)
17 Downloads (Pure)

Abstract

We analyse a simple correlation measure for tripartite pure states that we call G(A : B : C). The quantity is symmetric with respect to the subsystems A, B, C, invariant under local unitaries, and is bounded from above by log dA dB. For random tensor network states, we prove that G(A : B : C) is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with A, B, and C. We argue that for holographic states with a fixed spatial geometry, G(A : B : C) is similarly computed by the minimal area tripartition. For general holographic states, G(A : B : C) is determined by the minimal area tripartition in a backreacted geometry, but a smoothed version is equal to the minimal tripartition in an unbackreacted geometry at leading order. We briefly discuss a natural family of quantities Gn(A : B : C) for integer n ≥ 2 that generalize G = G 2. In holography, the computation of Gn(A : B : C) for n > 2 spontaneously breaks part of a ℤ n × ℤ n replica symmetry. This prevents any naive application of the Lewkowycz-Maldacena trick in a hypothetical analytic continuation to n = 1.

Original languageEnglish
Article number8
JournalJournal of High Energy Physics
Volume2023
Issue number5
Number of pages30
ISSN1126-6708
DOIs
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Keywords

  • AdS-CFT Correspondence
  • Black Holes in String Theory

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