Quantum Gravity Microstates from Fredholm Determinants

Abstract

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 , 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 of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions.