The non-perturbative phase diagram of the BMN matrix model

Abstract

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-$μ$, 3-loop perturbative, predictions. We find evidence that the transition at small $μ$ is to an M5-brane phase of the theory.