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Comments on black hole interiors and modular inclusions

by Ro Jefferson

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Ro Jefferson
Submission information
Preprint Link:  (pdf)
Date accepted: 2019-03-25
Date submitted: 2019-03-13 01:00
Submitted by: Jefferson, Ro
Submitted to: SciPost Physics
Ontological classification
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. 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.

Author comments upon resubmission

I would first like to thank the referee for their careful reading of the manuscript. Their report reflects precisely the key points I wished to convey, as well as the broader aim of the work, and I am delighted they found it of interest. The referee has made some helpful suggestions for improving the clarity of the paper, particularly by highlighting a few statements which could generate confusion; I have responded to these requested changes in detail in the "List of Changes" accompanying this resubmission. I am also grateful to the referee for catching the misspelling of "analogous". The instance of "found" in the third paragraph of section 5 is however correct as written (it is used here in the sense of "to ground, base, or establish").

I believe these changes have improved the manuscript, and thank the referee again for their detailed report.

Incidentally, as a matter of professional policy, I would like to politely object to the use of the masculine pronoun in requested change #2. While I do not believe the referee intended to misgender me, it is precisely for this reason that the gender of the author(s) should never be assumed. Rather, gender-neutral terms such as "the author" or the singular "they" should be used instead. The referee rightly does this throughout the rest of the report, but I believe this is nonetheless important to mention in the interest of cultivating a more inclusive scientific culture.

List of changes

In response to the referee's requested changes:

1. This is not a classical vs. quantum statement, but merely an attempt to emphasize the global definition of event horizons---namely, that contrary to existing depictions in the literature, the deformation does not cause the observer to hop out of the black hole. I agree with the referee that simply putting "inside" in quotations marks was ambiguous, particularly in light of the firewall debate, and have slightly modified both instances thereof on pages 4-5 in order to clarify my meaning.

2. While the meaning of exterior operators is discussed in more detail later in the manuscript, I have elaborated upon this first instance in an effort to mitigate any initial confusion.

3. I have broken the rather lengthy paragraph into two, as per the referee's sensible suggestion.

4. The referee is correct; I have modified the sentence to avoid such unintentionally cryptic phrasing.

Published as SciPost Phys. 6, 042 (2019)

Reports on this Submission

Anonymous Report 1 on 2019-3-20 (Invited Report)


I would like to thank the author for the time taken to properly address the small list of requested changes. I do recommend publication in its current format.

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