Black Holes and Thermodynamic States of Matrix Models

Abstract

Some recent work on the thermodynamic behavior of the matrix model of M-theory on a pp-wave background is reviewed. We examine a weak coupling limit where computations can be done explicitly. In the large N limit, we find a phase transition between two distinct phases which resembles a "confinement-deconfinement" transition in gauge theory and which we speculate must be related to a geometric transition in M-theory. We review arguments that the phase transition is also related to the Hagedorn transition of little string theory in a certain limit of the 5-brane geometry.

The confining transition in the bosonic BMN matrix model

“…When the mass parameter µ is very large, the model reduces to a solvable (gauged Gaussian) model. A straightforward calculation [6,7,29] shows that, in the large-N limit, there is a single phase transition with critical temperature…”

“…This family of quantum matrix models has a surprisingly rich phase structure including confining/deconfining phase transitions [5][6][7][8][9] as the temperature is varied.…”

“…When the mass parameter, µ, of the model is large the model reduces to a gauged Gaussian model, which is easily solved and has an apparent first-order confining/deconfining phase transition [6,7]. This transition would continue to smaller µ and based on the gauge/gravity duality conjecture for two-dimensional maximal SYM it should be connected to the Gregory-Laflamme [10,11] transition in the dual gravitational theory at zero mass deformation.…”

“…Its supergravity dual was studied in[33] 7. In the matrix model of this sector studied in[31,32,34] the transition only occurs for sufficiently negative quadratic term.…”

The nonperturbative phase diagram of the bosonic BMN matrix model

“…This family of quantum matrix models, which can also be interpreted as models of interacting D0-branes, has a surprisingly rich phase structure including deconfining phase transitions as the temperature is varied [5,6,7,8,9,10].…”