# Bulk entanglement entropy in perturbative excited states

### Submission summary

 As Contributors: Alexandre Belin · Nabil Iqbal · Sagar F. Lokhande Arxiv Link: https://arxiv.org/abs/1805.08782v2 (pdf) Date submitted: 2018-06-28 02:00 Submitted by: Lokhande, Sagar F. Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### Abstract

We compute the bulk entanglement entropy across the Ryu-Takayanagi surface for a one-particle 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 non-trivial check in a state where the answer is not dictated by symmetry. Along the way, we provide closed-form expressions for the scalar field Bogoliubov coefficients that relate the global and Rindler slicings of AdS$_3$.

### Ontology / Topics

See full Ontology or Topics database.

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

### Submission & Refereeing History

Resubmission 1805.08782v3 on 5 September 2018

Submission 1805.08782v2 on 28 June 2018

## Reports on this Submission

### Anonymous Report 1 on 2018-8-10 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1805.08782v2, delivered 2018-08-10, doi: 10.21468/SciPost.Report.552

### Strengths

1-Performing explicit computations. It is rare that the quantum corrections to the holographic entanglement entropy formula are explicitly computed.

### Weaknesses

1-A minor weakness is that analytic computations are done only in the small interval limit.

2-The 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 two-dimensional 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

1-In 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 $\varphi$.

2-There should be $\frac{1}{1-n}\log$ in eq. (2.12). Also in (2.15), (2.17), (2.21) etc.

• validity: high
• significance: good
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent

### Author:  Sagar F. Lokhande  on 2018-08-29

(in reply to Report 1 on 2018-08-10)
Category:
remark
correction

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.