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.
released 2026-09-24 | 1 theorem · 21 lemmas · 31 proofs · 21,153 words |
PLAY LEVEL 1 »(pdf)
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.
released 2026-10-05 | 1 theorem · 7 lemmas · 9 proofs · 4,255 words |
PLAY LEVEL 2 »(pdf)
We prove that the relative $\mathop{\mathrm{SU}}\nolimits (2)$ BFSS Hamiltonian has infinitely many positive eigenvalues tending to infinity, with square-integrable eigenvectors. The operator is defined by closing the gauge-invariant supercharge form. This refutes, at N = 2, the exclusion of normalizable positive-energy states stated in the original BFSS paper.