Related papers: Quantum Jackiw-Teitelboim gravity, Selberg trace f…
We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. We focus on the quantum mechanics of the model at past and future infinity. There is a Hilbert space of asymptotic states and…
We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these are holographically described by a deformation of the Schwarzian theory where the reparametrization mode is integrated over different coadjoint orbits of the…
We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the…
It is proposed that a complete understanding of two-dimensional quantum gravity and its emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) and 't Hooft (geometry). Using non-perturbative definitions of…
We formulate the path integral for Jackiw-Teitelboim gravity in the second order formalism working directly with the metric and the dilaton. We consider the theory both in Anti-de Sitter(AdS) and de Sitter space(dS) and analyze the path…
We study the BRST quantization of the 1+1 dimensional gravity model proposed by Jackiw and Teitelboim and also the topological gauge model which is equivalent to the gravity model at least classically. The gravity model quantized in the…
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…
The formulation of two-dimensional quantum gravity at finite cutoff remains an open problem. We revisit this question in JT gravity from two perspectives: the closed-channel bulk path integral and the path integral over boundary curves.…
I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes…
We prove that if $H$ denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph $(X,b,m)$, and if $v:X\to \mathbb{R}$ is such that $H+v/\hbar$ is well-defined as a form sum for all…
This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In…
We propose a refined expression for the large genus asymptotics of the Weil-Petersson volumes of the moduli space of super-Riemann surfaces with an arbitrary number of boundaries. Our formula leverages the connection between JT supergravity…
We continue the systematic study of the thermal partition function of Jackiw-Teitelboim (JT) gravity started in [arXiv:1911.01659]. We generalize our analysis to the case of multi-boundary correlators with the help of the boundary creation…
We consider Minkowskian Jackiw-Teitelboim (JT) gravity in Bondi gauge at finite temperature, with non-zero vacuum energy. Its asymptotic symmetries span an extension of the warped Virasoro group, dubbed "BMS$_2$", which we investigate in…
This undergraduate thesis is concerned with developing the tools of differential geometry and semiclassical analysis needed to understand the the quantum ergodicity theorem of Schnirelman (1974), Zelditch (1987), and Colin de Verdi\`ere…
We study the theory of Jackiw-Teitelboim gravity with generalized dilaton potential on Euclidean two-dimensional negatively curved backgrounds. The effect of the generalized dilaton potential is to induce a conical defect on the…
Motivated by recent analogies between the large-$q$ cSYK model and charged black holes, we aim to find a concrete gravitation theory with a matching partition function. Our main focus is to match the thermodynamics of the…
We consider a gravitational perturbation of the Jackiw-Teitelboim (JT) gravity with an arbitrary dilaton potential and study the condition under which the quadratic action can be seen as a $T\bar{T}$-deformation of the matter action. As a…
We present a coordinate-free background space construction of Euclidean Jackiw-Teitelboim gravity. It is written as a gauge theory that utilizes the Killing vectors and conformal Killing vectors of a hyperboloid embedded in a three…
We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The…