SciPost Submission Page
Witten index of BMN matrix quantum mechanics
by Chi-Ming Chang
Submission summary
| Authors (as registered SciPost users): | Chi-Ming Chang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202510_00008v1 (pdf) |
| Date accepted: | Nov. 11, 2025 |
| Date submitted: | Oct. 7, 2025, 6:02 a.m. |
| Submitted by: | Chi-Ming Chang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We compute the Witten index of the Berenstein-Maldacena-Nastase matrix quantum mechanics, which counts the number of ground states as well as the difference between the numbers of bosonic and fermionic BPS states with nonzero spins. The Witten index sets a lower bound on the entropy, which exhibits an $N^2$ growth that predicts the existence of BPS black holes in M-theory, asymptotic to the plane wave geometry. We also discuss a relation between the Witten index in the infinite $N$ limit and the superconformal index of the Aharony-Bergman-Jafferis-Maldacena theory.
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
Changes addressing the first report: 1. In the paper, the Witten index is computed using the Hamiltonian formalism. We added footnote 1, which comments on the computation in the path integral formalism that relies on the analytic continuation from Lorentzian to Euclidean signature. 2. We improved the paragraph containing Equations (2.15) - (2.17). Equation (2.15) does not need to be updated. We just need to regard $x^a_{kl,jm}$ as an $n_k\times n_l$ matrix. 3. We improved the paragraph on page 7. We added (2.18), which includes the bi-fundamental character, and renamed $z_{kl}$, $\iota_{kl}$ as the colorless single-letter BPS partition function and index (respectively). 4. We changed wording to “provides strong evidence”, “strongly suggests”, and “may correspond to”. We added footnote 4 to emphasize the properties of the small black holes in AdS5. 5. We corrected all the spelling and grammar that we can find.
Changes addressing the second report: 1. We improved paragraph 3 on page 2. 2. We added (2.48) to clarify the meaning of the divergent factor. Unfortunately, we do not have anything more to add about the resolution of this discrepancy and the further matching beyond the irreducible vacuum sector. This is why we leave this for future work.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
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Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)