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.
Highlights
Small dimensionless temperature τ this theory is dual to 11-dimensional supergravity in the following black hole geometry1
We study the thermodynamics of a massive deformation of the matrix quantum mechanics (1.1)
Our main result is the construction of the black hole geometry dual to the deconfined phase of the PWMM
Summary
Let us start by fixing our conventions for the bosonic piece of the 11-dimensional SUGRA action. The physical solution will be obtained from (2.2) by multiplying the metric by r02 and the 3-form C by r03, and by changing the period of the non-contractible M-theory circle according to ζ ∼ ζ + 2π. Both operations are symmetries of the equations of motion, but change the value of the on-shell action to r09 16πGN gs s r0. We need to appropriately turn on the 3-form potential C This is implemented in the Ansatz (2.2) by requiring the function M = M (x, y) to have the following asymptotic behaviour.
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