Gravity in Two Spacetime Dimensions

Abstract

In this habilitation thesis we provide an introduction to gravitational models in two spacetime dimensions. Focus is put on exactly solvable models. We begin by introducing and motivating different possible gravitational actions, including those of generalized dilaton theories as well as of purely geometrical, higher derivative theories with and without torsion. The relation among them as well as to Poisson sigma models is worked out in some detail. In the exactly solvable cases, such as pure gravity-Yang-Mills systems, the general solution to the field equations on a global level is reviewed. Quantization of such models is performed in the Dirac approach, where, by use of the formulation as Poisson sigma models, all admissible physical quantum states are obtained. Table of contents: 1. Introduction, 2. 2d geometry and gravitational actions, 3. Generalized dilaton theories and matter actions, 4. 2d gravity-Yang-Mills systems in terms of Poisson sigma models, 5. Classical solutions on a local level, 6. Classical solutions on a global level, 7. Towards quantum gravity. (In part this work contains/summarizes previous joint work with T. Kloesch and P. Schaller).

224 pages, 35 figures, Habilitation thesis RWTH Aachen, May 1999

References in corpus (8)

• Deformation quantization of Poisson manifolds, I
• A Uniqueness Theorem for Constraint Quantization
• On the relation between 2+1 Einstein gravity and Chern Simons theory
• A Brief Introduction to Poisson Sigma-Models
• The classical solutions of two-dimensional gravity
• Black Holes in Two Dimensions
• Poisson Structure Induced Field Theories and Models of 1+1 Dimensional Gravity
• General Treatment of All 2d Covariant Models

Cited by in corpus (23)

• Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
• Deformed General Relativity and Effective Actions from Loop Quantum Gravity
• Covariance in models of loop quantum gravity: Spherical symmetry
• Critical evaluation of common claims in loop quantum cosmology
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• Gravity from Lie algebroid morphisms
• Quantization of the Jackiw-Teitelboim model
• The Complete Solution of 2D Superfield Supergravity from graded Poisson-Sigma Models and the Super Pointparticle
• Hamiltonian BRST deformation of a class of n-dimensional BF-type theories
• Supergravity in Two Spacetime Dimensions
• Long time black hole evaporation with bounded Hawking flux
• Multi-exponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models
• PT-symmetry breaking hamiltonian interactions in BF models
• Nonsingular black hole in two-dimensional asymptotically flat spacetime
• On the generalized Freedman-Townsend model
• Group-valued momentum maps for actions of automorphism groups
• Generalized dilaton gravity in 2d
• Interacting mixed-symmetry type tensor gauge fields of degrees two and three: a four-dimensional cohomological approach
• Second Law of Black Hole Mechanics for all 2d Dilaton Theories
• Two-Dimensional Dilaton Gravity and Toda - Liouville Integrable Models
• Poisson sigma models on surfaces with boundary: classical and quantum aspects
• Discrete Linear Canonical Evolution
• Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity