Thermodynamics of the BMN matrix model at strong coupling

TL;DR

This paper constructs a gravity dual for the deconfined phase of the BMN matrix model at strong coupling, analyzing phase transitions and symmetry breaking as temperature varies.

Contribution

It provides a new black hole geometry dual to the BMN matrix model's deconfined phase at strong coupling, including phase transition details.

Findings

Identified the black hole geometry with $SO(9)$ symmetry at high temperature.

Determined the critical temperature for the confinement-deconfinement transition.

Described symmetry breaking from $SO(9)$ to $SO(6) imes SO(3)$ as temperature decreases.

Abstract

We construct the black hole geometry dual to the deconfined phase of the BMN matrix model at strong 't Hooft coupling. We approach this solution from the limit of large temperature where it is approximately that of the non-extremal D0-brane geometry with a spherical $S^8$ horizon. This geometry preserves the $SO(9)$ symmetry of the matrix model trivial vacuum. As the temperature decreases the horizon becomes deformed and breaks the $SO(9)$ to the $SO(6)\times SO(3)$ symmetry of the matrix model. When the black hole free energy crosses zero the system undergoes a phase transition to the confined phase described by a Lin-Maldacena geometry. We determine this critical temperature, whose computation is also within reach of Monte Carlo simulations of the matrix model.