The non-perturbative phase diagram of the BMN matrix model

TL;DR

This paper investigates the phase structure of the BMN matrix model at finite temperature, identifying phase transitions and their relation to gauge/gravity predictions, including evidence for an M5-brane phase at low mass parameter.

Contribution

It provides the first non-perturbative phase diagram of the BMN matrix model, connecting perturbative predictions with gravity duals and identifying phase transitions involving fuzzy spheres and M5-branes.

Findings

Identifies two phase transitions at high and low temperatures.

Shows the phase boundary approaches gravity predictions as b0 decreases.

Provides a Pade9 resummation estimate for transition points.

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 Pad\'e 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.