Consistency Conditions for Non-Perturbative Completions of JT Gravity

This is a careful examination of the key components of a large $N$ random matrix model method for going beyond ordinary JT gravity's topological expansion to define non-perturbative physics. It is offered as a simple and (hopefully) clear framework within which any proposed non-perturbative definition should fit, and hence be readily compared to others. Some minimal requirements for constructing consistent non-perturbative formulations are emphasized. A family of non-perturbative completions emerges from this, which includes an earlier construction. End-of-the-World branes, or simply D-branes, emerge straightforwardly in this framework and play a natural role. The many-body fermion picture of the matrix model is a key organizing motif, with many features highly analogous to a quantum black hole system, including a size that grows with the number of its microscopic constituents and a locus (the Fermi surface) beyond which quantities are traced over in order to define the physics. A formula for the thermal density matrix is proposed that allows a von Neumann form for the entropy to be written in matrix model terms.