Random Matrix Models, 2D Quantum Gravity, and Holography (Part 1)
In the first of two lectures I will present a pedagogical exploration of perhaps the simplest random matrix model, the Gaussian Unitary Ensemble. It gives the Airy model in the double scaling limit. I will first review the features that we usually focus on when studying models of gravity and argue that they need to be supplemented by much more non-perturbative information, readily computed using Fredholm determinants. The physical picture that emerges implies a specific kind of discrete spectrum, apparently previously unnoticed in this context. Its holographic meaning is discussed. This all readily generalizes to an infinite family of models.
Princeton University and University of Southern California