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NearExtremal Limits of Warped Black Holes
by Ankit Aggarwal, Alejandra Castro, Stéphane Detournay, Beatrix Mühlmann
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Authors (as registered SciPost users):  Ankit Aggarwal · Alejandra Castro 
Submission information  

Preprint Link:  https://arxiv.org/abs/2304.10102v1 (pdf) 
Date submitted:  20230424 15:20 
Submitted by:  Aggarwal, Ankit 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
A holographic description of threedimensional warped black holes suffers from ambiguities due to a seemingly harmless choice of coordinate system. This gives rise to the notion of ensembles in warped black holes, and we focus on two of them: the canonical and quadratic ensemble. Our aim is to quantify the imprint of these ensembles in the nearextremal limit of a warped black hole. To this end, for each ensemble, we explore the thermodynamic response and evaluate greybody factors. We also setup a holographic dictionary in their nearAdS$_2$ region, and decode aspects of the dual nearCFT$_1$. This gives us different perspectives of the black hole that we can contrast and compare. On the one hand, we find perfect agreement between the nearextremal limit of the canonical ensemble warped black holes, their nearAdS$_2$ effective analysis, and a warped conformal field theory description. On the other, we are led to rule out the quadratic ensemble due to inconsistencies at the quantum level with the nearAdS$_2$ effective description.
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Report
In this paper the authors study the holographic implications of having different descriptions or ensembles of a WCFT. It is known that WCFT admit different descriptions, dubbed “canonical” and “quadratic,” related by a statedependent coordinate transformation. These ensembles give rise to different warped black hole solutions and it is natural to ask how to single out which description is consistent with WAdS/WCFT holography. To answer this question, the authors focus on the nearextremal limit of warped black holes that are solutions of topological massive gravity and the holographic dictionary in their nearAdS2 region.
The authors analyze thermodynamic quantities, correlation functions and construct a low energy effective theory that describes the nearextremal dynamics of warped black holes and contains a JT sector.
The authors show that at the classical level both descriptions (canonical and quadratic) are equally good. But when looking at quantum corrections to the entropy, only the canonical description agrees with the predictions obtained from fieldtheoretical analysis of the nearextremal limit of WCFT.
The paper is interesting and adds to the warped black hole literature; I recommend it publication. Below are a couple of suggestions that I think will improve the presentation.
1)To find a solution to the metric perturbation, equation 5.30, the authors turn off
the homogeneous part of the field $\mathcal{F}$. While this is fine to study thermodynamics, $\mathcal{F}_{hom}$ is a massive degree of freedom that could lead to instabilities.
The authors do have a footnote on page 35 about this point. But I think the reader would be better served if this issue is discussed in the body of the paper and not relegated to a footnote.
2)Typos:
page 24: way from extremality > away from extremality
page 25: grebody > greybody
page 31: it useful > it is useful
Strengths
1systematically studies and compares the results of warped AdS3 black holes from three perspectives: topologically massive gravity in three dimensions, warped CFTs, and nearAdS2 dynamics
2finds a way to distinguish the canonical ensemble and quadratic ensemble of WCFT
3rules out the quadratic ensemble, and hence removes an ambiguity in the holographic duality for warped AdS3 black holes
Report
Warped AdS3 black holes share some features of BTZ black holes and also some features of Kerr black holes in four dimensions. Hence they are useful toy models to describe Kerr black holes holographically. The paper attempts to understand a longstanding ambiguity in the holographic description of warped AdS3 black holesthe choices of different ensembles. To do so, the paper systematically studies warped AdS3 black holes from three perspectives: topologically massive gravity in three dimensions, warped CFTs, and nearAdS2 dynamics.
It is found that the quadratic ensemble is ruled out by considering the logarithmic correction to the entropy. Both the topic and the conclusion are interesting and relevant. The paper is organized and written in a clear and concise way. I recommend the paper to be published in Scipost provided that the authors can make the requested changes listed below. Please note that point1 is an essential one, and has to be clarified in a satisfactory way .
Requested changes
1 The asymptotic Killing vectors eq. (2.15) in this paper seem to agree with eq. (14) and eq. (15) in arXiv 0808.1911, with N=1, N'=1. If so, the asymptotic algebra eq. (2.17) seems to be different from eq. (17) of arXiv 0808.1911. The authors should clarify this.
2 The paper arXiv 1407.7871 found a set of boundary conditions under which two copies of Virasora algebras were found for warped AdS3. This reference should be added as a piece of evidence of WAdS/CFT2.
3a typo on page 41: "a expected holographic dual">"an expected holographic dual"
Author: Ankit Aggarwal on 20230614 [id 3731]
(in reply to Report 2 on 20230604)
We would like to thank the referee for the positive review. We will implement the changes requested in points 2) and 3) in the revised version.
About point 1): The asymptotic Killing vectors in eq. (2.15) of our paper agree with eq. (14) and eq. (15) in arXiv 0808.1911, where one needs to take N=0, N’=1 (and not N=1, N’=1 as stated in the report). Therefore the asymptotic algebra eq. (2.17) agrees with (17) of arXiv 0808.1911. We hope this clarifies this point.
Author: Ankit Aggarwal on 20230710 [id 3793]
(in reply to Report 4 on 20230707)We would like to thank the referee for the positive remarks and comments. Regarding the two points:
1) We completely agree that this is an important point. We will incorporate footnote 15 in the paragraph below eqn (5.38). We also note that the last paragraph of the conclusion (page 43) also discusses the instability.
2) The typos will be fixed in the resubmission.