Quantum Gravity Microstates from Fredholm Determinants.

Various two dimensional quantum gravity theories of Jackiw-Teitelboim (JT) form have descriptions as random matrix models. Such models, treated nonperturbatively, can give an explicit and tractable description of the underlying "microstate" degrees of freedom, which play a prominent role in regimes where the smooth geometrical picture of the physics is inadequate. This is shown using a natural tool, a Fredholm determinant det(1-K), which can be defined explicitly for a wide variety of JT gravity theories. To illustrate the methods, the statistics of the first several energy levels of a nonperturbative definition of JT gravity are constructed explicitly using numerical methods, and the full quenched free energy F_{Q}(T) of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions.