Thermal bootstrap of large-N matrix models via conic optimization

A bstract This paper is aimed at improving thermal bootstrapping methods for matrix quantum mechanics. The thermal energies of the large- N one-matrix anharmonic oscillator and large- N two-matrix anharmonic oscillator are bounded without logarithmic relaxation using the Quantum Information Conic Solver. For the one-matrix model, which can be interpreted using an effective theory of “long strings” in the low temperature limit, stricter bootstrap bounds yield a value of the first long string excited energy within 0 . 001% of the physical value and the first estimation from symmetry and self-consistency equations alone of the first long string coupling coefficient.