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Looking at supersymmetric black holes for a very long 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/2207.00408v3 (pdf) |
| Date accepted: | 2023-03-29 |
| Date submitted: | 2023-02-10 01:43 |
| Submitted by: | Lin, Henry |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study correlation functions for extremal supersymmetric black holes. It is necessary to take into account the strongly coupled nature of the boundary supergraviton mode. We consider the case with ${\cal N}=2$ supercharges which is the minimal amount of supersymmetry needed to give a large ground state degeneracy, separated from the continuum. Using the exact solution for this theory we derive formulas for the two point function and we also give integral expressions for any $n$-point correlator. These correlators are time independent at large times and approach constant values that depend on the masses and couplings of the bulk theory. We also explain that in the non-supersymmetric case, the correlators develop a universal time dependence at long times. This paper is the longer companion paper of arXiv:2207.00407.
Published as SciPost Phys. 14, 128 (2023)
Henry Lin on 2023-02-19 [id 3377]
Dear Editor,
We apologize for mistakenly not including the response to the referees in the resubmission. Below we include it (and the attached PDF which has the revisions.)
In response to the optional questions raised by referee 1: 1) We do not see an obvious relation with the Aretakis instability. 2) The bulk dilaton is discussed briefly in the section on entanglement entropy. Classically, the dilaton goes to S_0, but our matter computation shows that the entropy is corrected due to quantum effects. 3) We have rewritten section 5.1 for clarity.
In response to the technical comments: 1,2) We have corrected the equation (22) and also thank the referee for finding the other typos. We have also corrected numerous other minor typos in this revision, including some sign errors that were pointed out to us.
In response to referee 2:
We thank the referee for Looking at our paper for a very long time. 1) We have amended both this paper and its shorter companion paper to clarify the meaning of \Delta. We have added some comments in the beginning of section 2 and an associated footnote. We also refer the reader to section 5.5 for clarification.
2)The entanglement entropy indeed is invariant under a unitary transformation of just one boundary, whereas the simple correlation functions that we discuss are sensitive to 1-sided unitaries. Presumably a sufficiently complicated unitary can destroy the simple 2-sided correlations. One could imagine acting on one side by exp(iJO) where O is one of the matter operators; we expect from the OTOC discussion that this should increase the length mode and therefore decrease the 2-sided correlators.
3) We do not have a clear bulk interpretation of x and y. At best one can say that we have modified the usual ADM Hamiltonian so that it corresponds to the projected operator, but we do not have a simple picture associated to this statement. Our main point in introducing them was to demonstrate that the eigenvalues of the projected matter operators behave like random matrices.
4) We have clarified this point right after equation (131).
Attachment:
DraftNTwo-compressed.pdf