Toy Models of Quantum Gravity

Abstract

In this dissertation we use simple models of quantum gravity to study the AdS/CFT correspondence. The main focus is on Jackiw-Teitelboim (JT) gravity, an exactly solvable two-dimensional model. We first show how to enrich JT gravity with dynamical End-of-the-World (EoW) branes. Upon integrating out the branes, an additional term is added to the effective action of the metric and dilaton, and the change in the semiclassical black hole entropy has a state-counting interpretation consistent with the number of brane species. A novel feature of our analysis is that EoW branes contribute to UV divergences, which we regulate in the gravitational theory and the dual matrix model. Another way to generate UV divergences in JT gravity is to add a minimally coupled scalar field. We introduce a single-trace, two-matrix model that computes all of the disk correlators of this theory for all times. The two matrices may be interpreted as a Hamiltonian and a boundary operator that is dual to the bulk field. We also discuss the double-trumpet in this matrix model. Next, we turn our attention to Lorentzian JT gravity without matter and explain how the Ryu-Takayanagi formula may be used to compute the entanglement entropy of an arbitrary pure state to all orders in Newton’s constant. We show that the algebra of bulk observables in an entanglement wedge admits a modified trace that is needed to correctly compute gravitational entanglement entropies in Lorentzian signature. Finally, we generalize a theorem due to Harlow that relates bulk entanglement entropy computations to the quantum error-correcting properties of holographic theories.