High-precision bootstrap of multi-matrix quantum mechanics

Abstract: We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$ in the confining phase of the theory in the infinite $N$ limit. By leveraging the symmetries of these models and using non-linear relaxation, we consider constraints up to level 14, e.g., constraints from traces of words of length $\le 14$. Our results are more precise than large $N$, continuum extrapolations of lattice Monte Carlo simulations, including an estimate of certain simple observables up to 8 significant digits.