Download or read book Progress in Low-dimensional Anti-de Sitter Gravity written by Matthew Hodel and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "We discuss recent developments in theories of quantum gravity in two and three spacetime dimensions.We begin by considering the Jackiw-Teitelboim (JT) theory, a model of pure 2d gravity, providing a new perspective on a perturbative expansion in the quantum version of this theory, inspired by random matrix theory. Random matrix theory (RMT) captures universal properties of the very late-time dynamics of an extremely wide class of chaotic quantum systems. JT gravity goes farther by agreeing precisely with a random matrix ensemble, beyond universal quantities. We take a Lagrangian approach to quantization of JT theory. We find that we must perform path integrals over 2d geometries of arbitrary genus. Integrating first over the dilaton field restricts to constant negative curvature surfaces. A connection is made with the topological recursion relations of Eynard and Orantin, which allow the computation of such path integrals for arbitrary-genus surfaces by cutting them apart into pairs of pants. The resulting asymptotic series for JT observables matches onto the genus expansion familiar from random matrix theory.Recent work has also appeared deriving a boundary graviton description of pure AdS3 gravity. Pure gravity was thought for some time to be trivial in three spacetime dimensions since there are no local graviton degrees of freedom. Nevertheless global effects render the theory nontrivial. We will use standard path integral methods to approximate the gravity partition function around a semiclassical background geometry. The resulting boundary graviton scalar field action describes global excitations around background AdS3 spacetime. It serves as a 2d generalization of the 1d Schwarzian theory, which itself describes boundary fluctuations of the JT theory"--