Bootstrapping supersymmetric (matrix) quantum mechanics

A bstract 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 D 0 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 ~ κg 2/3 scaling of E with g and extract a lower bound on the coefficient κ &gt; .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 = $$ \sqrt{2}{g}_c $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> . We attribute this to truncation error and solver limitations, and discuss possible improvements.