The nonperturbative phase diagram of the bosonic BMN matrix model

We study the thermal phase transition of the bosonic BMN model which is a mass deformed version of the bosonic part of the BFSS model. Our results connect the massless region of the phase diagram described by the bosonic BFSS model with the large-mass region, where the model is analytically solvable. We observe that at finite value of the matrix size N, the critical region is smeared over a small temperature range. The model has a single critical temperature, this arises as the large N limit of two apparent transitions at finite N. We emphasise the vital role played by finite N corrections in the confined phase and illustrate this with a novel treatment of the noninteracting Gaussian model.