Bootstrapping supersymmetric (matrix) quantum mechanics

• URL: http://arxiv.org/abs/2510.01356v1
• Date: Wed, 01 Oct 2025 18:35:27 GMT
• Title: Bootstrapping supersymmetric (matrix) quantum mechanics
• Authors: Samuel Laliberte, Brian McPeak,
• Abstract summary: We apply the quantum-mechanics bootstrap to supersymmetric quantum mechanics (SUSY QM) and to its matrix relative, the Marinari-Parisi model.<n>Using positivity of moment matrices together with Heisenberg, gauge, and (zero-temperature) thermal constraints, we obtain rigorous bounds on ground-state data.<n>We find a spurious kink at $g = sqrt2 g_c$ where the two wells merge into one.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We apply the quantum-mechanics bootstrap to supersymmetric quantum mechanics (SUSY QM) and to its matrix relative, the Marinari-Parisi model, which is conjectured to describe the worldvolume of unstable $D0$ branes. Using positivity of moment matrices together with Heisenberg, gauge, and (zero-temperature) thermal constraints, we obtain rigorous bounds on ground-state data. In the cases where SUSY is spontaneously broken, we find bounds that apply to the lowest-energy normalizable eigenstate. For $N = 1$ SUSY QM with a cubic superpotential, we obtain tight bounds that agree well with available approximation methods. At weak coupling they match well with the semiclassical instanton contribution to SUSY-breaking ground-state energy, while at strong coupling they exhibit the expected scaling and match well with Hamiltonian truncation. For the SUSY matrix QM, we construct a $44 \times 44$ bootstrap matrix and obtain bounds at large $N$. At strong coupling, we obtain the expected $E \sim \kappa \ g^{2/3}$ scaling of $E$ with $g$ and extract a lower bound on the coefficient $\kappa > .196$. At small coupling, the theory has a critical point $g_c$ where the two wells merge into one. We find a spurious kink at $g = \sqrt{2} g_c$. We attribute this to truncation error and solver limitations, and discuss possible improvements.

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