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The unique threshold bound state of the SU(N) BFSS model
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Abstract
For every finite N ≥ 2, we prove that undeformed $\mathop{\mathrm{SU}}\nolimits (N)$ BFSS matrix quantum mechanics has exactly one normalizable zero-energy state after removing the center of mass. This establishes the threshold-bound-state conjecture.
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Possibly relevant literature (found by the agent, not checked)
- W. Krauth, H. Nicolai, M. Staudacher, Monte Carlo Approach to M-Theory (arXiv:hep-th/9803117, Phys. Lett. B 431 (1998) 31-41). Numerically evaluates the zero-dimensional SYM partition functions behind the bulk index and supports extending the Green–Gutperle conjecture to SU(3); relevant to the paper's account of bulk and boundary index contributions.
- J. Hoppe, D. Lundholm, M. Trzetrzelewski, Spin(9) Average of SU(N) Matrix Models I. Hamiltonian (arXiv:0809.5271, J. Math. Phys. 50 (2009) 043510). Uses Spin(9) group averaging on the SU(N) matrix-model Hamiltonian; relevant to the paper's statement that the kernel consists of Spin(9)-invariant states (Theorem 1.1).
- Seung-Joo Lee and Piljin Yi, Witten Index for Noncompact Dynamics (arXiv:1602.03530, 2016). Its treatment of the distinction between infrared-regulated partition functions and the physical $L^2$ Witten index is relevant to the manuscript’s passage from a massive index to the undeformed normalizable kernel.
Elsewhere
- VibeMathed: Problem record
- Emergent Mind: family 270
Independent sites; their content is not reviewed here.
Cite
@misc{OAI:The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026,
author = {{OpenAI}},
title = {{The unique threshold bound state of the $\mathrm{SU}(N)$ BFSS model}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026/paper.pdf}{OAI:The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026}},
year = {2026}
}Family 270: Threshold and positive-energy bound states of the BFSS matrix model
Proves that the undeformed relative $\mathrm{SU}(N)$ BFSS model has exactly one normalizable zero-energy state for every finite N ≥ 2, resolving the threshold-bound-state conjecture. For $\mathrm{SU}(2)$, a companion proves infinitely many normalizable positive-energy eigenstates with unbounded energies, contradicting the original BFSS paper's exclusion of additional bound states at N = 2.
Other papers in this family:
- Positive eigenvalues of the relative SU(2) BFSS Hamiltonian · October 5, 2026