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Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index
by Sunjin Choi, Diksha Jain, Seok Kim, Vineeth Krishna, Goojin Kwon, Eunwoo Lee, Shiraz Minwalla, Chintan Patel
Submission summary
| Authors (as registered SciPost users): | Diksha Jain |
| Submission information | |
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| Preprint Link: | scipost_202503_00041v2 (pdf) |
| Date submitted: | July 11, 2025, 2:33 p.m. |
| Submitted by: | Jain, Diksha |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
Motivated by the recent construction of grey galaxy and Dual Dressed Black Hole solutions in AdS5×S5, we present two conjectures relating to the large N entropy of supersymmetric states in N=4 Yang-Mills theory. Our first conjecture asserts the existence of a large number of supersymmetric states which can be thought of as a non interacting mix of supersymmetric black holes and supersymmetric `gravitons'. It predicts a microcanonical phase diagram of supersymmetric states with eleven distinct phases, and makes a sharp prediction for the supersymmetric entropy (as a function of 5 charges) in each of these phases. The microcanonical version of the superconformal index involves a sum over states - with alternating signs - over a line in 5 parameter charge space. Our second (and more tentative) conjecture asserts that this sum is dominated by the point on the line that has the largest supersymmetric entropy. This conjecture predicts a large N formula for the superconformal index as a function of indicial charges, and predicts a microcanonical indicial phase diagram with nine distinct phases. It predicts agreement between the superconformal index and black hole entropy in one phase (so over one range of charges), but disagreement in other phases (and so at other values of charges). We compare our predictions against numerically evaluated superconformal index at N≤10, and find qualitative agreement.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
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In response to referee 1, we added Appendix A on the unobstructed saddle conjecture, giving an example where it fails and another example where it works. We explained why we expect it to work in the physical situation.
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In response to referee 1, we have improved the explanation of the fact that the gas lies within the bosonic cone in section 2.8 and Appendix B.5. We have also improved Table 2 (the improved table now carries more fine grained information about the charges of all single trace operators; the final column in the table can be used to verify our claim that the charges of all bosonic single trace operators lie in the bosonic cone, in the manner explained in the new Footnote 43). We have also corrected some minor errors in Appendix B.6.
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In response to Referees 2 and 3, we added an Appendix I (and subsections 2.4 and 2.6) on the manifestation of our new phases in the Canonical Ensemble. As the material of this new Appendix contains the material of Appendix B.4 in our previous version, we have removed Appendix B.4 in this version.
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In response to referee 1, we added section 5.3.1 to explain oscillations in Figure 17. The oscillations are coming from the imaginary part of the entropy.
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In response to referee 1, we added the words "(and more tentative)" in the abstract. We have also emphasized the limited a priori evidence for the unobstructed saddle conjecture in the newly written text under the statement of the conjecture (in subsection 1.3 of the introduction).
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In the process of addressing the referees' questions and comments, we have also taken the opportunity to fix additional typos and grammatical mistakes, etc, that caught our eye.
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The new additions to the draft have been flagged at appropriate places in the updated introduction and discussion sections.
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However, I have some comments on the newly added Appendix. A.3. The authors state there: "The number of black hole states as a function of charge is expected to be determined by diagonalizing a ‘one loop’ Hamiltonian that is expected to display features of chaos". They interpret this as saying that the number of BPS states has some random fluctuations as a function of charges.
I believe that the Hamiltonian exhibiting chaos does not imply that the number of black hole states display any randomness. One way to probe this question is to ask whether the number of BPS states, for a fixed charge, would have small random fluctuations if one consider an ensemble of Hamiltonians within the same symmetry class. If the starting Hamiltonian is sufficiently generic such that all the BPS states that could be lifted are already lifted, the BPS spectrum should not fluctuate at all.
Within a fixed theory, we can ask what we expect from the gravity side. At the perturbative level, one should in principle be able to estimate the number of states by studying loop corrections of quantum fields on the BPS black hole background, and it is hard to see how this would produce genuine randomness. One might also wonder about non-perturbative corrections, but there is an independent gravity argument (see around (2.3) in https://arxiv.org/pdf/2307.13051) that the degeneracy of BPS states does not receive wormhole corrections.
The authors refer to [45] in the quote. As far as I understand, the chaos they were studying is the chaos of BPS wavefunctions rather than the number of states.
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