Information, Geometry, and Physics Seminar

Feynman's recipe for quantum mechanics states that a physical quantity may be computed by integrating over "paths" that could contribute to that quantity. This approach is very successful in quantum field theory, but fails completely for General Relativity, where naively we must integrate over an uncontrollable set of spacetime manifolds. In this talk, we will describe a situation where, despite the non-linearity of General Relativity, the path integral may be done exactly in some limit. This situation is that of a very low temperature black hole, and the relevant degrees of freedom are the metric fluctuations near the horizon. The path integral which computes the black hole partition function may be rewritten in terms of a topological field theory, and ultimately the black hole entropy is computed by the Duistermaat–Heckman localization formula. This gives corrections to Hawking's famous area formula, and generalizing this result leads to a classification of black holes based on their preserved (super)-symmetries.