Bootstrapping supersymmetric (matrix) quantum mechanics
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arXiv
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| Format: | Preprint |
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2025
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| author | Laliberte, Samuel McPeak, Brian |
| author_facet | Laliberte, Samuel McPeak, Brian |
| contents | 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 $E \sim κ\ g^{2/3}$ scaling of $E$ with $g$ and extract a lower bound on the coefficient $κ> .196$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bootstrapping supersymmetric (matrix) quantum mechanics Laliberte, Samuel McPeak, Brian High Energy Physics - Theory Mathematical Physics Quantum Physics 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 $E \sim κ\ g^{2/3}$ scaling of $E$ with $g$ and extract a lower bound on the coefficient $κ> .196$. 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. |
| title | Bootstrapping supersymmetric (matrix) quantum mechanics |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.01356 |