# Entanglement Wedge in Flat Holography and Entanglement Negativity

### Submission summary

 As Contributors: Debarshi Basu · Vinayak Raj · Gautam Sengupta Preprint link: scipost_202107_00038v2 Date submitted: 2021-11-03 08:40 Submitted by: Sengupta, Gautam Submitted to: SciPost Physics Core Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual $(1+1)$-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual $AdS/CFT$ scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.

###### Current status:
Has been resubmitted

We have examined the referee report for our submission scipost_202107_00038v1 entitled Entanglement Wedge in Flat Holography and Entanglement Negativity". We would like to thank the referee for the interesting questions and comments. Our detailed response to the issues raised and their resolutions are described in the reply to the referee's report. We have appropriately made the required changes to our manuscript as suggested by the referee.

### List of changes

We have provided the complete list of changes made in the authors response section.

### Submission & Refereeing History

Resubmission scipost_202107_00038v3 on 12 January 2022

Resubmission scipost_202107_00038v2 on 3 November 2021
Submission scipost_202107_00038v1 on 21 July 2021

## Reports on this Submission

### Report

I am the second referee; the paper has already gone through one round of review and revision.

I was asked by the editor to address a question concerning the computation of the negativity using twist operators. This computation was done in a different paper (ref 64 in the current draft). In the current paper the corresponding EWCSs were computed and compared to the results of that computation, finding agreement (up to some constant terms in the TMG case). While it is interesting to ask about the twist operator computations and their validity, in my view this question is not directly germaine to the issue of whether this paper ought to be published. Even if the twist operator computations turn out to be flawed, the EWCS computations of the current paper will still be valuable (perhaps even more so, since it could indicate a disagreement between the EWCS and negativity). Therefore I don’t think that this issue should prevent the current paper from being published.

I agree with the comments of the previous referee, and I also agree with their conclusion that the paper deserves to be published in SciPost.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Gautam Sengupta  on 2022-01-12  [id 2092]

(in reply to Report 2 on 2022-01-03)

We would like to thank Referee2 for the comments and for recommending publication.

### Report

I thank the authors for their revision and I am satisfied by their replies on the comments 1,3,4,5.

Especially, their reply on comment 3 gives interesting relation between the entanglement negativity (or the EWCS, reflected entropy) and the mutual information. This shows that, unlike the case in AdS/CFT, the so called Markov gap or crossing PEE vanishes in BMSFTs dual to the Einstein gravity (where the central charge $c_{L}=0$). This broadens the interestingness of the manuscript.

My only concern is still the comment 2. Originally, I just want the authors to specify that, those null rays in the geometric picture are the lines emanating from the boundary endpoints and moving along the bulk modular flow. In the Bondi gauge they are just lines along the r coordinate. However the authors introduced the "ambiguity" raised up by Ref. [63]. I cannot fully understand this “ambiguity”, because after a translation along the 'y' coordinate the image of the boundary interval no longer lines on the boundary at a constant 'r'. I kindly suggest the author to remove this part as it is controversial.

The manuscript is significantly improved and I am happy to recommend it for publication.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Gautam Sengupta  on 2022-01-12  [id 2093]

(in reply to Report 1 by Qiang Wen on 2021-11-13)

We would like to thank Referee1 for the comments and for recommending publication. As per the Referee's suggestion we have removed the part described as controversial by the Referee in the resubmitted manuscript.