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Threshold and positive-energy bound states of the BFSS matrix model
Proves that the undeformed relative BFSS model has exactly one normalizable zero-energy state for every finite N ≥ 2, resolving the threshold-bound-state conjecture. For , 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.
Manuscripts in this family · 2
The unique threshold bound state of the SU(N) BFSS model
Sep 24, 2026·paper.pdf
For every finite N ≥ 2, we prove that undeformed BFSS matrix quantum mechanics has exactly one normalizable zero-energy state after removing the center of mass. This establishes the threshold-bound-state conjecture.
Positive eigenvalues of the relative SU(2) BFSS Hamiltonian
Oct 5, 2026·positive-eigenvalues-relative-su2-bfss.pdf
We prove that the relative 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.