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Bulk entanglement entropy in perturbative excited states
by Alexandre Belin, Nabil Iqbal, Sagar F. Lokhande
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Submission summary
As Contributors:  Alexandre Belin · Nabil Iqbal · Sagar F. Lokhande 
Arxiv Link:  https://arxiv.org/abs/1805.08782v2 (pdf) 
Date submitted:  20180628 02:00 
Submitted by:  Lokhande, Sagar F. 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We compute the bulk entanglement entropy across the RyuTakayanagi surface for a oneparticle state in a scalar field theory in AdS$_3$. We work directly within the bulk Hilbert space and include the spatial spread of the scalar wavefunction. We give closed form expressions in the limit of small interval sizes and compare the result to a CFT computation of entanglement entropy in an excited primary state at large $c$. Including the contribution from the backreacted minimal area, we find agreement between the CFT result and the FLM and JLMS formulas for quantum corrections to holographic entanglement entropy. This provides a nontrivial check in a state where the answer is not dictated by symmetry. Along the way, we provide closedform expressions for the scalar field Bogoliubov coefficients that relate the global and Rindler slicings of AdS$_3$.
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Reports on this Submission
Anonymous Report 1 on 2018810 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1805.08782v2, delivered 20180810, doi: 10.21468/SciPost.Report.552
Strengths
1Performing explicit computations. It is rare that the quantum corrections to the holographic entanglement entropy formula are explicitly computed.
Weaknesses
1A minor weakness is that analytic computations are done only in the small interval limit.
2The authors confirm only numerically that the change of entanglement entropy by an excitation in the CFT side agrees with the FLM formula.
Report
The authors compute the shift of entanglement entropy by an excitation in large c twodimensional CFT, and compare the results to the bulk quantities proposed by Faulkner, Lewkowycz and Maldacena. In the AdS side, the bulk reduced density matrix is obtained in the mode expansion form, and the shift of the bulk entanglement entropy is computed in the small interval limit. The shift of the minimal area by back reaction is also evaluated. Combining them, the authors numerically find the agreement between the CFT result and the bulk result. It is a wonderful and important work. I recommend the paper for publication.
However, I would like to request the authors to fix some typos listed below.
Requested changes
1In eq.(2.11), it seems that $\theta$ should be replaced by $\theta/n$. It is better to write the definition of $z$ in eq.(2.10) in terms of $\varphi$.
2There should be $\frac{1}{1n}\log$ in eq. (2.12). Also in (2.15), (2.17), (2.21) etc.
Author: Sagar F. Lokhande on 20180829 [id 310]
(in reply to Report 1 on 20180810)We thank the referee for their kind words and careful reading of the draft.
We agree with the assessment of weaknesses and hope that in future work we can overcome the technical difficulties in analytic continuations.
Regarding the requested changes: 1. Indeed, there is a 1/n missing in (2.11) which we have fixed. There was also a typo in (2.10) which we have corrected which we believe addresses the referee's concerns. 2. We have corrected these typos.