General Treatment of All 2d Covariant Models

TL;DR

This paper provides a comprehensive analysis of all 2D covariant gravity models, including their solutions, global structures, and potential for quantization, with extensions to matter fields.

Contribution

It offers a unified framework for 2D covariant gravity models, detailing their solutions, global structures, and methods for deriving actions from manifolds.

Findings

Complete solutions for all models are known.

Arbitrary singularity structures can be studied.

Quantization and conservation laws are analyzed.

Abstract

General matterless models of gravity include dilaton gravity, arbitrary powers in curvature, but also dynamical torsion. They are a special class of "Poisson-sigma-models" whose solutions are known completely, together with their general global structure. Beside the ordinary black hole, arbitrary singularity structures can be studied. It is also possible to derive an action "backwards", starting from a given manifold. The role of conservation laws, Noether charge and the quantization have been investigated. Scalar and fermionic matter fields may be included as well.