AdS/CFT, black holes and matrix models

This talk is based on papers [1, 2], where the reader is sent for details and references. The main theme is associated with the fact that many properties of Black Holes (at least in AdS space-times) can be cast in terms of properties of N = 4 supersymmetric Yang-Mills Theory according to the Maldacena conjecture. In particular thermal properties of black holes can be translated into thermal properties of supersymmetric field theories. In [5] it is shown how one can reformulate properties of black holes in terms of certain types of unitary matrix models, and the simples examples are considered in detail. In [1] we generalize the models presented in [5] and show that under certain reasonable conditions one can reproduce the properties of the Hawking-Page transition, and the Hagedorn temperature in term of some specific matrix models, making some universality assumptions. The string interpretation close to the singularities associated to the various critical points are analyzed and studied in detail using Matrix Model technology. In [2] we reconsider the problems treated in [1, 5] and we analyze it in the most general possible thermal effective action of the gauge theory on a three sphere. With some mild assumptions we understand the behavior of the small, unstable black holes in AdS in terms of the Horowitz-Polchinski transitions from Black Holes to and AdS background with a gas of highly excited thermal strings.