Positive-energy bound states in the SU(2) BFSS model
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Does the relative SU(2) BFSS Hamiltonian have square-integrable gauge-invariant eigenvectors at positive energies? The operator is defined by closure of its supercharge quadratic form.
Why it matters and what counts as progress
Why it matters: Positive-energy bound states test a spectral assertion different from the zero-energy threshold-state question.
What counts as progress: A normalizable positive eigenstate, or an exclusion theorem for the same self-adjoint Hamiltonian; an unbounded orthonormal sequence of such eigenstates is a stronger result.
How the problem developed
- 7 Oct 1996 · Conjecture [1]
Tom Banks, Willy Fischler, Stephen H. Shenker and Leonard Susskind Proposed matrix quantum mechanics as a nonperturbative description of M-theory, establishing the BFSS model whose spectrum is studied here.
- 5 Oct 2026 · Proof claim [2]
OpenAI Released a manuscript claiming an unbounded sequence of positive square-integrable gauge-invariant eigenvalues for the relative SU(2) BFSS Hamiltonian.
AI contribution
Positive eigenvalues of the relative SU(2) BFSS Hamiltonian
For the relative SU(2) BFSS Hamiltonian defined by closing its supercharge quadratic form, the manuscript claims an orthonormal sequence of square-integrable gauge-invariant eigenvectors with positive eigenvalues tending to infinity.
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Publication dates and editorial changes.
OpenAI reports positive-energy states in the SU(2) BFSS model