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”.