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.

Manuscripts (2)

The unique threshold bound state of the SU(N) BFSS model

September 24, 2026 · source · cite as \cite{OAI:The-unique-threshold-bound-state-of-the-SU-N-BFSS-model-September-24-2026}

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.

Positive eigenvalues of the relative SU(2) BFSS Hamiltonian

October 5, 2026 · source · cite as \cite{OAI:Positive-eigenvalues-of-the-relative-SU-2-BFSS-Hamiltonian-October-5-2026}

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.

Result 270 · Mathematical physics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.