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Radiation, entanglement and islands from a boundary local quench
by Lorenzo Bianchi, Stefano De Angelis, Marco Meineri
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Authors (as registered SciPost users):  Lorenzo Bianchi · Stefano De Angelis · Marco Meineri 
Submission information  

Preprint Link:  scipost_202206_00032v1 (pdf) 
Date submitted:  20220627 19:45 
Submitted by:  De Angelis, Stefano 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study the entanglement and the energy density of the radiation emitted after a local quench in a boundary conformal field theory. We use the operator product expansion (OPE) to predict the early and latetime behaviour of the entanglement entropy and we find, under mild assumptions, a universal form for the leading term, which we test on some treatable twodimensional examples. We also derive a general upper bound on the entanglement, valid along the full time evolution. In two dimensions, the bound is computed analytically, while in higher dimensions it is evaluated at early and late time via the OPE. These CFT predictions are then compared with a doublyholographic setup where the CFT is interpreted as a reservoir for the radiation produced on an endoftheworld brane. After finding the gravitational dual of a boundary local quench, we compute the time evolution of the holographic entanglement entropy, whose latetime behaviour is in perfect agreement with the CFT predictions. In the brane+bath picture, unitarity of the time evolution is preserved thanks to the formation of an island. The holographic results can be recovered explicitly from the island formula, in the limit where the tension of the brane is close to the maximal value.
Current status:
Reports on this Submission
Anonymous Report 2 on 202299 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202206_00032v1, delivered 20220909, doi: 10.21468/SciPost.Report.5673
Strengths
See below
Weaknesses
See below (basically none!)
Report
This is a very wellwritten paper that discusses a topic of great current interest; it begins with a study from conformal field theory of the entanglement entropy during a quench in the presence of a boundary. In particular, the authors make use of 2d conformal invariance to both:
a) derive universal formulas for the EE at late times, given some assumptions on the defect operator spectrum, and
b) derive bounds on the growth of this quantity using general properties of the EE.
This result is of intrinsic interest to the EEinmanybodyphysics community. However the authors then go on to discuss the holographic dual; I found the discussion to be very complete and provide a wealth of detail on how to construct the solutions from different points of view. The authors find agreement with general CFT expectations; finally they also show that the result can be viewed as support for the “Island” prescription if one considers a duality frame where the bulk of AdS_{3} is considered in a fieldtheoretical duality frame, but the brane itself is considered in a dynamical gravity duality frame. (This agreement is expected along the lines of recent work in Refs [33, 34], but it is still nice to see in a slightly new kinematics).
I found this paper to be extremely wellwritten, timely, and providing a wealth of detail. Though none of its conclusions are very unexpected, the detailed computations and CFT results are quite valuable. I can find little to improve and recommend publication in its current form.
Requested changes
Nothing.
Strengths
Well written, very clear and easy to follow. Interesting results.
Weaknesses
None, other than the small clarifications present in my report.
Report
See report attached.
Author: Stefano De Angelis on 20230207 [id 3331]
(in reply to Report 1 on 20220903)
We would like to thank the referee for a careful reading of our paper and for the insightful comments. We made some improvements in various parts of our work to address the points raised in the report.

The referee asked about the gravitational interpretation of the relative entropy bound. While addressing this question, we took the occasion to delve in more detail into the microscopic origin of the universal part of the entanglement entropy as well. We extended the discussion in sections 3.2, 3.3.1, 4.1, and 5.3. In Section 3.2 and 3.3.1, we show that the sl(2) block of the displacement operator coincides with the relative entropy bound. In section 4.1, after eq. 4.12, we refined the microscopic interpretation of the universal part of the entropy (i.e. the bound) as the total contribution of single copy operators in the replica orbifold. Incidentally, section 4.1 has been slightly reorganised: for additional clarity, we defined a conformal map that sends the upper half plane into itself (see the new figure 9) and rephrased the computation in terms of the latter. Finally, we come to the holographic interpretation of the bound at the end of section 5.3. The discussion after eq. 5.45 is new, including figure 16: there, we make closer contact with the previous results in the literature, and we point out that the bound acquires a clear holographic interpretation in the limit where the excitation above the vacuum becomes light.

We agree that the comment about the operator O being singletrace was confusing, and we have removed it.

We agree with the referee and point his/her attention to the last comment before section 5.1, which we added in the revised version. We also make the microscopic interpretation of the holographic entanglement entropy in terms of the Virasoro module of the identity completely precise, in section 5.3.

The inequality is correct. In this section, we consider Delta >> c, which is needed in equation 5.53 and makes possible the definition of the local temperature in terms of the CFT data (equation 5.57). We added a clarification at the beginning of the section.

The references suggested by the referee and few more others have been added.

We have also taken the chance to correct some typos in the text.
Author: Stefano De Angelis on 20230207 [id 3332]
(in reply to Report 2 on 20220909)We would like to thank the referee for their accurate assessment of our paper and for their positive evaluation.