Thermal Bootstrap of Large-N Matrix Models via Conic Optimization

Abstract

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 were 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.