Interacting Euclidean 3D Quantum Gravity

TL;DR

This paper demonstrates that Euclidean 3D quantum gravity coupled with a scalar field has a finite perturbative expansion around a non-zero background and explores mechanisms to generate non-trivial backgrounds from loop observables.

Contribution

It introduces a finite perturbative quantum gravity model with matter and proposes a method to derive non-trivial backgrounds from loop observables.

Findings

Finite perturbative expansion around a non-zero background

Coupling of 3D gravity with scalar matter field

Potential mechanism for background generation from loop observables

Abstract

We show that Euclidean 3D-gravity coupled to a Gaussian scalar massive matter field in first-order dreibein formalism gives a quantum theory which has a finite perturbative expansion around a non-vanishing background. We also discuss a possible mechanism to generate a non-trivial background metric starting from Rovelli-Smolin's loop observables.