Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

TL;DR

This paper investigates the classical solutions and quantum properties of 2D Euclidean dilaton gravity, revealing topological restrictions and performing non-perturbative path integral quantization, with detailed analysis of Liouville gravity.

Contribution

It provides a comprehensive classification of classical solutions and a non-perturbative quantization approach for 2D Euclidean dilaton gravity, including a detailed study of Liouville gravity.

Findings

All local classical solutions are obtained.

Only certain topologies are consistent with the metric and dilaton.

Non-perturbative path integral quantization is achieved.

Abstract

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.