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 $(\mu ,T)$ plane, where $\mu$ 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 $\mu >3.0$ there is a second distinct transition at a lower temperature. The two transitions approach one another at smaller $\mu$ and merge in the vicinity of $\mu =3.0$. The resulting single transition curve then approaches the gauge/gravity prediction as $\mu$ is further decreased. We find a rough estimate of the transition, for all $\mu$, is given by a Padé resummation of the large-$\mu$, 3-loop perturbative, predictions. We find evidence that the transition at small $\mu$ is to an M5-brane phase of the theory.

arXiv commentminor corrections, typos fixed, acknowledgements updated

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• Confinement/deconfinement transition in the D0-brane matrix model -- A signature of M-theory?
• Thermal phase transition in Yang-Mills matrix model
• Three-dimensional super-Yang--Mills theory on the lattice and dual black branes
• Lattice studies of supersymmetric gauge theories
• Partial Deconfinement at Strong Coupling on the Lattice
• Statistical Physics of the Polarised IKKT Matrix Model
• The Confining Transition in the Bosonic BMN Matrix Model
• Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model
• Axial Anomaly in the $SU(N)$ Gauge Matrix Model
• Chaotic Dynamics of the Mass Deformed ABJM Model
• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Witten index of BMN matrix quantum mechanics
• Finite-temperature phase diagram of the BMN matrix model on the lattice
• A Charge Constraint in BMN
• Non-perturbative phase structure of the bosonic BMN matrix model