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Puzzles and pitfalls involving Haar-typicality in holography
by Ning Bao, Aidan Chatwin-Davies
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Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.
Published as SciPost Phys. 4, 033 (2018)
Author comments upon resubmission
List of changes
- The changes described in our reply and that we made in v4 were brought forward to v5. The sentence that we added in the introduction was moved to a footnote on p.3, and the new section 5.3 remains in-place.
- We added the heuristic example to section 5.3. We did not include our detailed rebuttal in the draft, as it is publicly-visible on this submission page.
- We amended the text throughout to remove any use of the term "Haar-typical state of a CFT". (This includes a revision to the abstract.) We agree with the referee that the term is ill-defined---Haar-typicality indeed requires a finite-dimensional Hilbert space.
- We further highlight this point in the 6th paragraph of the introduction, and we cleaned up the rest of this paragraph accordingly.
- Likewise, we re-wrote section 2 starting at the last paragraph on p.4 to be more careful about the finite-dimensional Hilbert space that is to be used in place of the full continuum CFT for defining Haar-typicality. Rather than focus on a specific lattice model, we elected to write down what properties we assume for a finite-dimensional model and we give several examples of models with these properties in the literature, including the critical spin chain.
- We acknowledged the subtlety that the referee raised regarding the relationship between UV cutoffs in the bulk and boundary in a footnote on p.5.
- We made small aesthetic formatting changes and corrected minor typos throughout.
- We also added several references.
Submission & Refereeing History
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