Holography
Juan Maldacena, Institute for Advanced Studies

In physics there are two broad types of theories. On the one hand we have theories defined on a fixed spacetime. These describe particles that propagate and interact with each other. On the other hand, we have theories where spacetime itself is dynamical, such as Einstein’s theory of gravity. Particle theories can be described in a fully quantum mechanical fashion using quantum field theory. Theories of quantum gravity are a bit more mysterious, but they can be described by string theory.

In certain circumstances, the full theory of quantum gravity can be completely equivalent to certain quantum field theories. This happens in certain negatively curved spacetimes. Such spacetimes have a ``boundary’’ at infinity. The particles of the quantum field theory live on this boundary at infinity. The spacetime interior emerges dynamically. We can think of these particles as the elementary ``atoms’’ which are making a quantum spacetime.

This picture relates everything that happens in the interior to something on the boundary theory. In particular, if we have a black hole in the interior, there is a corresponding state on the boundary theory. In fact, the black hole corresponds to a thermal configuration on the boundary theory. Thus, black hole thermodynamics is translated into the ordinary thermodynamics of the boundary theory. This can be used to learn about quantum aspects of black holes. It can also be used to learn about systems of strongly interacting particles. Simple computations around a black hole background can give us information about the interior theory.

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