Extremality as a Consistency Condition on Subregion Duality

Based on the explicit computation in the context of JT gravity, the paper aims to demonstrate that the boundary of entanglement wedge being the Q.E.S follows naturally from the general self-consistency conditions of subregion dualities known as CCWE (complementary causal wedge exclusion). To make progress, a few additional assumptions were imposed regarding properties of the bulk dual in relation to CCWE. The paper is an interesting attempt to provide novel understanding of the emergence of entanglement wedge in the context of subregion dualities.

In my opinion, the paper in the current form possibly needs additional streamlining regarding the presentation, including the choice of notations etc. I do have the following naïve question regarding the argument, that I hope the author can address and explain in better terms. A crucial ingredient in the argument is to use the bulk dual of the connes-cocycle flow to construct counter-examples that would violate CCWE, if the bulk subregion is not bounded by the Q.E.S. It is unclear to me whether there is a possibility of cyclic logic here, since the known bulk dual of the connes-cocyle flow, i.e. in terms of bulk shock waves, is based on entanglement wedge reconstruction. Maybe I have missed some important steps here. Naively it seems that to avoid cyclic logic in the arguments, one needs an understanding of the bulk dual of the connes cocycle flow for the "off-shell” choice of bulk subregions — whatever that means. Some comments in this respect will be ideal for facilitating the understanding of the readers.

Ask for minor revision

This paper argues that the entanglement wedge is bounded by the QES. Comparing with the old argument, the advantage of this paper is that it is purely in Lorentz picture. This paper studies an important question and provides inspiring discussions. Based on this reason, I suggest the paper to be published.

Publish (meets expectations and criteria for this Journal)

1- very interesting result
2- clear exposition
3- clear study of assumptions

This is a very nice paper that shows under some carefully studied assumptions that the entanglement wedge of a boundary subregion in JT coupled to a CFT must be bounded by a QES. By computing the Connes cocycle unitary of a boundary state with respect to the vacuum, the author is able to violate the property of complementary causal wedge exclusion in the case where the region is bounded by anything else than a QES, which leads to a contradiction.

I found the derivation in this paper interesting as it provides a very geometric and completely Lorentzian understanding of why a QES has special recovery properties. I also think the paper is careful with its assumptions and provides an extensive and honest analysis of where they might break down (especially in the case with islands). Therefore I am happy to recommend this paper for publication in SciPost.

Publish (easily meets expectations and criteria for this Journal; among top 50%)