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Entanglement Negativity and Defect Extremal Surface
by Yilu Shao, MaKe Yuan, Yang Zhou
Submission summary
Authors (as registered SciPost users):  Yang Zhou 
Submission information  

Preprint Link:  https://arxiv.org/abs/2206.05951v2 (pdf) 
Date submitted:  20230906 06:51 
Submitted by:  Zhou, Yang 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study entanglement negativity for evaporating black hole based on the holographic model with defect brane. We introduce a defect extremal surface formula for entanglement negativity. Based on partial reduction, we show the equivalence between defect extremal surface formula and island formula for entanglement negativity in AdS$_3$/BCFT$_2$. Extending the study to the model of eternal black hole plus CFT bath, we find that black holeradiation negativity follows Page curve, black holeblack hole negativity decreases until vanishing, radiationradiation negativity increases and then saturates at a time later than Page time. In all the time dependent cases, defect extremal surface formula agrees with island formula.
Current status:
Author comments upon resubmission
List of changes
1. Added a detail explanation of eq.(58) in footnote 10.
2. In footnote 6 we added some detail discussion about the 3/2 factor of eq.(28). We also improved Figure 3 to illustrate the reduction of RT surface and the origin of the 2d area term.
3. Added a discussion of reflected entropy in footnote 3.
4. Corrected the text about doubling trick around eq.(50), eq.(135), and in the caption of Figure 4.
5. Improved Figure 11 to clarify that we are focusing on the left system in Section 7.3. We also added some explanations in Section 7.3.
6. Corrected a typo in eq.(131) where a twopoint function was miswritten as a threepoint function. We also added explanations about the factorization after eq.(131).
7. Appendix A was deleted.
8. We also corrected many English as well as a few typos of the previous version.
Submission & Refereeing History
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Report
In the revised version, the authors have satisfactorily addressed some of the issues raised in the previous report. However several other issues have not been addressed or the explanations are not satisfactory as listed below. This also includes specific suggestions to resolve the issues which have been raised.
Given the outstanding issues I suggest that the authors specifically address these in another revised version. I will be happy to recommend publication in SciPost Physics Core once the above issues are satisfactorily resolved.
Requested changes
1. The authors have completely ignored the issue raised regarding the absence of the inherent CFT on the brane originating from the RS reduction. In this article, the CFT on the brane is purely the defect CFT which they have introduced and the contribution from the inherent CFT is missing. Explanation about such behaviour needs to be provided from the Karch Randall construction.
2. The authors have removed the usage of doubling trick for the conversion of the 2point BCFT correlator to a 3point chiral CFT correlator utilized in eqs. (50,135,142). I understand that such factorizations work and provide the correct matching with the bulk results, however some explanation about this behaviour is still needed.
3. Regarding the changes made in section 7.3, the authors have removed the labelling for the point $O'$ present earlier in their diagrams. However, as stated earlier, the correlation function required to compute the entanglement negativity for adjacent intervals should have twist operators at the endpoints of both the subsystems under consideration making it of the form $\left<\mathcal{T}_n (A)\bar{\mathcal{T}}^2_n(Q) \mathcal{T}_n (O')\right>$. As the extent of the left black hole region should be dynamically determined, the correct entanglement negativity should be obtained by extremizing over the point $O'$ whose contribution cannot be ignored.
4. The authors have again ignored the next issue raised in the previous report. In eqs. (134,135), a 4point twist correlator in a CFT is converted to a 3point twist correlator through the doubling and inverse doubling trick. However, the said twist operators are placed in the TFD copies and should not be regarded as BCFT correlators. Thus the application of doubling and inverse doubling trick is invalid for such a correlator. The authors should justify the factorization through a conformal block expansion of the twist correlator from a CFT (without any boundary) approach.
5. On the issue regarding the OPE coefficient for the relevant 3point twist correlator, the authors have removed the said appendix. However, they still claim in eq. (17) that the OPE coefficient remains unchanged. We believe unless a derivation of this fact along the lines of appendix C in reference [76] is provided, this remains as an assumption which should be clearly stated in the manuscript.