UC Berkeley

This thesis will be an exploration of various topics within low dimensional quantum gravity,with an emphasis on the gravitational path integral. We begin by studying two-dimensional Jackiw-Teitelboim (JT) gravity deformed by a gas of conical defects and we solve the model non-perturbatively. We then consider the problem of defining the Lorentzian gravity path integral through a contour rotation of the Euclidean path integral within the context of JT gravity. We demonstrate the agreement of integration domains and calculate the measure for the Lorentzian path integral. We then analyze ensemble averaging a family of two dimensional Conformal Field Theories and find a relation with an exotic three-dimensional bulk Chern-Simons theory.