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

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.

27 p., LaTeX, v2: included new refs. and a footnote

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Cited by in corpus (11)

• Thermodynamics of Black Holes in Two (and Higher) Dimensions
• Poisson sigma model on the sphere
• Quantization of the Jackiw-Teitelboim model
• Diffeomorphism covariant star products and noncommutative gravity
• Black Hole Thermodynamics and Hamilton-Jacobi Counterterm
• 2D holography beyond the Jackiw-Teitelboim model
• Duality in 2-dimensional dilaton gravity
• Physics-to-gauge conversion at black hole horizons
• Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals
• Discontinuous normals in non-Euclidean geometries and two-dimensional gravity
• Boundary Conditions for $\mathrm{Ad}{\mathrm{S}}_2$ Dilaton Gravity