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Holography for people with no time
by Henry W. Lin, Juan Maldacena, Liza Rozenberg, Jieru Shan
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Submission summary
Authors (as registered SciPost users):  Henry Lin 
Submission information  

Preprint Link:  https://arxiv.org/abs/2207.00407v2 (pdf) 
Date submitted:  20220813 02:45 
Submitted by:  Lin, Henry 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study the gravitational description of extremal supersymmetric black holes. We point out that the $AdS_2$ near horizon geometry can be used to compute interesting observables, such as correlation functions of operators. In this limit, the Hamiltonian is zero and correlation functions are time independent. We discuss some possible implications for the gravity description of black hole microstates. We also compare with numerical results in a supersymmetric version of SYK. These results can also be interpreted as providing a construction of wormholes joining two extremal black holes. This is the short version of a longer and more technical companion paper arXiv:2207.00408.
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Reports on this Submission
Report #2 by Anonymous (Referee 2) on 20221121 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2207.00407v2, delivered 20221121, doi: 10.21468/SciPost.Report.6168
Strengths
Overall a nice summary (companion) paper with interesting results.
Weaknesses
Sometimes a little hard to understand without looking at the longer paper at the same time.
Report
The authors study correlation functions in extremal black holes with N=2 supersymmetry, using the exact description of the AdS2 near horizon geometry. In the zero energy limit, quantum gravity effects are large and a finite number of degenerate ground states separated from the continuum by a gap, lead to twopoint functions with a constant large time limit. The boundary description in this limit is `topological' in the sense that the Hamiltonian disappears and the full time reparametrization symmetry is restored. Various implications on topics of current interest are discussed.
The results are very interesting and timely. The paper is often quite schematic. I think this is ok in this particular case because it is a companion paper to a longer paper, which contains more details. The question is then whether this companion paper deserves to be published separately. I believe the answer is definitely yes, as this manuscript does offer a nice summary of the results and presents them in a useful way. Also, some of the discussion (such as microstates) is more detailed here than in the long paper.
Sometimes the paper is a bit hard to follow, which is not the desired purpose of a companion paper. E.g., section 2.7 (which contains content that's not in the long paper) could perhaps be expanded a bit to make it more selfcontained (e.g. the "West Coast model" is mentioned without further explanation or reference). Similarly, the discussion of correlation functions around (17)(19) is perhaps a bit too schematic and hard to follow without consulting the longer paper. It would be good if this could be expanded a bit.
Report #1 by Anonymous (Referee 1) on 20221121 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2207.00407v2, delivered 20221121, doi: 10.21468/SciPost.Report.6164
Strengths
Good paper exploring some important implications of quantum effects in supersymmetric black holes.
Weaknesses
Relies on companion paper for details, some aspects are hard to comprehend.
Report
The paper explores an interesting class of observables in supersymmetric black holes by focusing attention on the nearhorizon region. The authors argue that natural observables are correlation function of operators inserted on the boundary of the near horizon region, which by virtue of the nearAdS2 asymptotics and focus on the lowenergy or longtime limit, have timeindependent (constant) correlations. The paper is a summary of a companion paper and as such avoids the technical details. However, certain aspects of the discussion are somewhat hard to comprehend in the present manuscript. While I think the paper is of highquality and should be accepted for publication, I would like to encourage the authors to consider making it a bit more selfcontained. Some specific issues are highlighted below:
1. The thermofield double state used in the discussion could do with some clarification. Prior to taking the nearhorizon limit, the states are BPS (sticking to supersymmetric black holes), and one is usually led to consider the microcanonical ensemble of states in the BPS subspace of the Hilbert space. While I understand the thermofield double state to be the state obtained from the global AdS2 with its two boundaries, explaining how this is related to the UV description would be helpful. Relatedly, should the Hamiltonian specified in (1) which vanishes be seen as the BPS Hamiltonian of the UV description? While the authors are clear, I think it would also would help the casual reader to be aware that `boundary' always refers to the nearhorizon boundary.
2. A minor pedantic comment: Eq (7) as written is a bit strange. The l.h.s is a vector in Hilbert space, while the r.h.s appears to be a representation in a particular basis.
3. In Section 2.5 are the Lorentzian correlations still restricted to the boundary of the AdS2 region? Is the statement made here equivalent to saying that there is no response from the nearhorizon region. What correlations are captured by operators that are smeared over a timescale of order $1/E_{gap}$?
4. The discussion of composite operators in Section 2.6 is mildly confusing. In usual AdS CFT dictionary bulk fields correspond to primaries of the CFT. Descendants or multiparticle states are excitations of the same bulk field. Does this picture hold for the AdS2 region under discussion or is it modified to include new operators corresponding to multiparticle excitations?
5. Finally, it would be useful to have some brief comments on how the operators discussed in the nearhorizon region should be viewed from the UV perspective.