What the study found
The study found that the quantum-mechanics bootstrap can be applied to supersymmetric quantum mechanics (SUSY QM) and to the Marinari-Parisi matrix model, producing rigorous bounds on ground-state data. In cases where supersymmetry is spontaneously broken, the bounds apply to the lowest-energy normalizable eigenstate.
Why the authors say this matters
The authors suggest this matters because the Marinari-Parisi model is conjectured to describe the worldvolume of unstable D0 branes, and because the bounds provide information in regimes where other methods are compared against them. They also conclude that their results show promise for improving understanding of these quantum systems.
What the researchers tested
The researchers applied the quantum-mechanics bootstrap using positivity of moment matrices together with Heisenberg, gauge, and zero-temperature thermal constraints. They studied N = 1 SUSY QM with a cubic superpotential and the SUSY matrix quantum mechanics at large N, using a 44 × 44 bootstrap matrix.
What worked and what didn't
For N = 1 SUSY QM with a cubic superpotential, they obtained tight bounds that agreed well with available approximation methods. At weak coupling, the bounds matched the semiclassical instanton contribution to the supersymmetry-breaking ground-state energy, and at strong coupling they showed the expected scaling and agreed well with Hamiltonian truncation.
For the SUSY matrix quantum mechanics, the authors obtained large-N bounds and found the expected E ~ κg^2/3 scaling at strong coupling, with a lower bound on the coefficient κ greater than .196. At small coupling, they found a spurious kink at g = sqrt{2} g_c, which they attribute to truncation error and solver limitations.
What to keep in mind
The abstract says the kink is likely spurious and links it to truncation error and solver limitations. It also notes that the discussion includes possible improvements, but the available summary does not describe them in detail.
Key points
- The bootstrap method produced rigorous bounds on ground-state data for SUSY QM and the Marinari-Parisi matrix model.
- For N = 1 SUSY QM with a cubic superpotential, the bounds were tight and matched approximation methods well.
- In the weak-coupling regime, the bounds matched semiclassical instanton contributions to supersymmetry-breaking ground-state energy.
- For the matrix model at large N, the authors found the expected strong-coupling scaling E ~ κg^2/3 and a lower bound κ > .196.
- A spurious kink appeared at g = sqrt{2} g_c, which the authors attribute to truncation error and solver limitations.
Disclosure
- Research title:
- Bootstrap bounds constrain supersymmetric quantum mechanics
- Authors:
- Samuel Laliberte, Brian McPeak
- Institutions:
- Okinawa Institute of Science and Technology Graduate University, McGill University, Syracuse University
- Publication date:
- 2026-04-22
- OpenAlex record:
- View
- Image credit:
- Photo by Markus Winkler on Pexels · Pexels License
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