Bootstrap bounds on D0-brane quantum mechanics

We derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski's virial theorem bound to finite energies and gives the first non-trivial bound on $\langle{\text{Tr}\, X^2\rangle}$. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. Our best lower bounds are already a factor of $\sim 2$ from existing Monte Carlo results.