Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity

Abstract

Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D space-time dimensions.

31 pages

References in corpus (7)

• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Anomaly freedom in perturbative loop quantum gravity
• Loop quantum gravity corrections to gravitational wave dispersion
• Loop quantum cosmology and inhomogeneities
• Singularities and Quantum Gravity
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries