This thesis explores topics in two-dimensional quantum gravity, focusing on the specific model of Jackiw-Teitelboim (JT) gravity and its relation to higher-dimensional black holes (BHs). Such a study is motivated by (i) the fact that JT gravity is a full-fledged theory of quantum gravity and (ii) because problematic features in higher-dimensional gravity, such as those related to black holes or wormholes, can be addressed in two-dimensions.
Chapter 2 is based on work with Pufu, Y. Wang, and Verlinde. We propose an exact quantization of JT gravity by formulating the theory as a gauge theory. We find that this theory's partition function matches that of the Schwarzian theory. Observables are also matched: correlation functions of boundary-anchored Wilson lines in the bulk are given by those of bi-local operators in the Schwarzian.
Chapter 3 is based on work with Krutthof, Turiaci, and Verlinde. We compute the partition function of JT gravity at finite cutoff in two ways: (i) by evaluating the Wheeler-DeWitt wavefunctional and (ii) by performing the path integral exactly. Both results match the partition function in the Schwarzian theory deformed by the analog of the TT deformation in $2D$ CFTs, thus, confirming the conjectured holographic interpretation of TT.
In chapter 4, we study JT gravity coupled to Yang-Mills theory. When solely focusing on the contribution of disk topologies, we show that the theory is equivalent to the Schwarzian coupled to a particle moving on the gauge group manifold. When considering the contribution from all genera, we show that the theory is described by a novel double-scaled matrix integral.
Chapter 5 is based on work with Turiaci. We answer an open question in BH thermodynamics: does the spectrum of BH masses have a “mass gap” between an extremal black hole and the lightest near-extremal state? We compute the partition function of Reissner-Nordström near-extremal BHs at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge exhibits no gap; instead, we see a continuum of states at the expected gap energy scale.