Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity

TL;DR

This paper explores the connection between spherically symmetric gravity, dilaton models, and Poisson sigma models, introducing loop quantum gravity quantization and quantum corrections that deform the classical theory consistently.

Contribution

It presents a novel loop quantization of spherically symmetric models, incorporating quantum corrections and establishing a covariant action principle via Poisson sigma models.

Findings

Quantum corrections deform inverse triad components without anomalies.

Loop quantization extends to arbitrary D-dimensional spherically symmetric models.

Covariant action principle derived from Poisson sigma models for quantum-corrected theory.

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.