Bootstrapping supersymmetric (matrix) quantum mechanics

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 × 44 bootstrap matrix and obtain bounds at large N. At strong coupling, we obtain the expected E ~ κ\ g2/3 scaling of E with g and extract a lower bound on the coefficient $κ> .196$. At small coupling, the theory has a critical point gc where the two wells merge into one. We find a spurious kink at g = √2 gc. We attribute this to truncation error and solver limitations, and discuss possible improvements.