The non-perturbative phase diagram of the BMN matrix model

We study the maximally supersymmetric plane wave matrix model (the BMN model) at finite temperature, T, and locate the high temperature phase boundary in the (μ, T) plane, where μ is the mass parameter. We find the first transition, as the system is cooled from high temperatures, is from an approximately SO(9) symmetric phase to one where three matrices expand to form fuzzy spheres. For μ > 3.0 there is a second distinct transition at a lower temperature. The two transitions approach one another at smaller μ and merge in the vicinity of μ = 3.0. The resulting single transition curve then approaches the gauge/gravity prediction as μ is further decreased. We find a rough estimate of the transition, for all μ, is given by a Padé resummation of the large-μ, three-loop perturbative predictions. We find evidence that the transition at small μ is to an M5-brane phase of the theory.