Description
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 S8 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) ×
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. The scaling behaviour of the free energy, entropy and
horizon size earlier derived in the literature follows from
a simple scaling symmetry of the gravity action. We also
determine the asymptotic gravity data in terms of
normalizable modes near the boundary.
