# Juan M. Maldacena: Research Interests

In the past two years I have been doing research mainly on the description of black holes in string theory and on the relation of the large N limit of gauge theories and gravity. String theory is presently understood well enough to answer some of the puzzles of black hole physics. First I have been interested in calculating the entropy of black holes. Particularly, of black holes with nonzero Hawking temperature. It is possible to count the microscopic configurations that have the macroscopic properties of black holes. The description can be derived from string theory first principles and it does not involve any extra ad-hoc hypothesis. The result of this microscopic counting is, of course, the macroscopic Hawking-Beckenstein entropy that was calculated from general thermodynamic reasons 20 years ago. Furthermore, its decay rate can also be calculated precisely with the D-brane model. It is possible to understand the decay as a simple perturbative process. The advantage of the string theory approach is that the model is explicitly unitary, giving a description of black holes which obeys the basic principles of quantum mechanics. This model of black holes gives the correct decay rate, including its complicated functional dependence with the energy (the so called grey body factor).

Motivated by this relationship of D-branes and black holes I have proposed a duality between gauge theories and gravity. Twenty years ago 't Hooft had realized that gauge theories would simplify in the large N limit. In fact this duality provides the solution of the large N limit for the maximally supersymmetric gauge theory in four dimensions. It is surprising that this solution involves a *gravitational* system, namely anti-de-Sitter spacetimes, which were quite extensively analyzed in the past for other reasons. Several checks of this duality were done by doing calculations in the gauge theory which translate into apparently very different computations in the gauge theory and agreement was found. Using this large N duality black holes are related to the quark deconfinement transition. So the problem of understanding black holes was related to the problem of understanding large N gauge theories.

I am planning to continue exploring this surprising relationship with the aim of understanding the large N limit of QCD as well as the quantum aspects of gravity, including black holes. This duality has been extended to non-supersymmetric cases, but not yet to the case of pure QCD. Hopefully it will be possible to apply these methods to QCD too. Another interesting extension of these ideas would be to the precise quantum treatment of de-Sitter space-times, which represent expanding universes as in the inflationary phase of the early universe. I think that solid progress will be made in this direction, which will not only shed light on conceptual issues but also provide useful analytical tools to tackle these problems.