SciPost logo

SciPost Submission Page

Comments on black hole interiors and modular inclusions

by Ro Jefferson

This is not the current version.

Submission summary

As Contributors: Ro Jefferson
Arxiv Link: (pdf)
Date submitted: 2019-01-31 01:00
Submitted by: Jefferson, Ro
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


We show how the traversable wormhole induced by a double-trace deformation of the thermofield double state can be understood as a modular inclusion of the algebras of exterior operators. The effect of this deformation is the creation of a new region of spacetime deep in the bulk, corresponding to a non-trivial center between the left and right algebras. This set-up provides a precise framework for investigating how black hole interiors are encoded in the CFT. In particular, we use modular theory to demonstrate that state dependence is an inevitable feature of any attempt to represent operators behind the horizon. We suggest that this provides an ontological basis for the success of quantum error correction (QEC) in holography. Building on this geometrical structure, we propose that modular inclusions may provide a more precise means of investigating the nascent relationship between entanglement and geometry in the context of the emergent spacetime paradigm.

Ontology / Topics

See full Ontology or Topics database.

Black holes Conformal field theory (CFT) Entanglement
Current status:
Has been resubmitted

Submission & Refereeing History

You are currently on this page

Submission 1811.08900v2 on 31 January 2019

Reports on this Submission

Anonymous Report 1 on 2019-2-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1811.08900v2, delivered 2019-02-23, doi: 10.21468/SciPost.Report.843


1. Use of concepts in algebraic quantum field theory together with physical arguments to discuss aspects of black hole interiors and related matters.
2. The manuscript attempts to be self-contained.
3. The main goals of the manuscript go through.


1. Few statements may generate some confusions among the readers and some clarification may improve its readership.


The work “Comments on black hole interiors and modular inclusions” is a timely and interesting piece of work providing some insightful remarks on the interpretation of black hole interiors using tools from algebraic quantum field theory.

Looking at the manuscript as a whole, I believe the two main points made in this work : i) that state dependence is inherited from the requirement of describing the physics of the interior of BHs by imposing operators to be unitary and local (using the exterior algebra) and ii) to give evidence for the relevance of modular inclusions to describe traversable wormholes by enlarging the notion of exterior algebra, in a process that is kind of opposite to the one making it smaller, i.e. the one appearing in shock-wave physics as in Shenker-Stanford, do go through.

Even though the main technical remarks and proofs are rather abstract (building on notions developed in algebraic quantum field theory), the main body of the text always provides with physical arguments and interesting digressions/comparisons with existent arguments in the literature regarding bulk reconstruction, the construction of mirror operators and their state dependence, relation to quantum error correction and the language of code subspaces. The manuscript also makes an attempt at being self-contained by including a pair of appendices in which the Tomika-Takesaki theory is briefly reviewed and implications for relative entropy and mutual information discussed from both bulk and boundary perspectives are discussed.

Referencing is good.

To sum up, even though this is a topic with many open questions left and part of the content in this manuscript is reviewing material first introduced in other references, I find the perspective offered by modular inclusions insightful and gives the author the chance to provide good physical arguments commenting on previous work that some readers will find inspiring and clarifying. For all these reasons, I recommend to publish this manuscript in this journal, though it would benefit its readership if the author could act upon the points raised above.

For completeness, let me mention some typos : there are several “analagous” through the entire text that should be replaced by “analogous”. Furthermore, I believe the word “found” in page 18 in the paragraph ending with the footnote 22 should be replaced by “find”.

Requested changes

1. In section 2, when referring to the teleological nature of event horizons, it is claimed the double trace deformation does not allow information inside the black hole to escape because it would violate causality. I am not sure what the author is alluding to here. Perhaps this is related to the use of quotation marks for the word inside. Is this a classical statement ? How does Hawking-radiation fit into this statement ? It would help some readers if the author can explain this point in a slightly different way.
2. In section 2, and currently at the start of page 6, the notion of “exterior operators” is used. Though eventually there should be no doubt on what the author is referring to, it may help to define more precisely what they mean (operators belonging to the von Neumann algebras just introduced).
3. In section 2, I would suggest to break the long paragraph at the start of page 6. In particular, the sentence starting with “Lastly” where new notation is being introduced could easily be moved to a separate paragraph. In the current version, one is expecting a further argument to support the discussion one is reading about, but encounters some further notation ending with a definition.
4. In section 2, by the end of the first paragraph in page 8, I find the statement “more low-energy operators are required to effect the same back reaction” confusing. It seems to me the author wants to say more low-energy operators are required to encode the information of a larger amount of exterior spacetime, which makes perfect sense with the arguments presented. I would suggest to improve this sentence to prevent any confusions among the readers.

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Login to report or comment