Quantum Black Hole Physics from Random Matrix Models*

A large N random matrix model's spectral density is generically a continuous function. In the context of various 2D quantum gravity models where the matrix model reproduces the sum over geometry and topology, this has been taken to mean that the holographic dual neccessarily involves an ensemble of Hamiltonians. This has led to a great deal of interesting activity, exploring the idea that gravity may fundamentally be an ensemble in more general contexts. However, a closer look at the matrix models shows that a discrete structure is in fact present in the spectrum. It is a sum of energy peaks that can be computed using Fredholm determinant techniques. It is suggested that this discrete structure reveals the spectrum of the single dual Hamiltonian of the gravity theory, and hence that gravity is not dual to an ensemble. Holography for 2D gravity then more closely resembles higher dimensional holography. An alternative interpretation of the matrix models' sum over topologies is given. Since some of these 2D gravity models arise from the low temperature physics of classes of higher dimensional black holes, these results also shed light on their low temperature physics.