The BFSS model on the lattice

Abstract

We study the maximally supersymmetric BFSS model at finite temperature and its bosonic relative. For the bosonic model in $p+1$ dimensions, we find that it effectively reduces to a system of gauged Gaussian matrix models. The effective model captures the low temperature regime of the model including one of its two phase transitions. The mass becomes $p^{1/3}\lambda^{1/3}$ for large $p$, with $\lambda$ the 'tHooft coupling. Simulations of the bosonic-BFSS model with $p=9$ give $m=(1.965\pm .007)\lambda^{1/3}$, which is also the mass gap of the Hamiltonian. We argue that there is no `sign' problem in the maximally supersymmetric BFSS model and perform detailed simulations of several observables finding excellent agreement with AdS/CFT predictions when $1/\alpha'$ corrections are included.