Solvable model for quantum gravity

TL;DR

This paper introduces a geometric model with an $su(2)$ gauge field and one-forms, serving as a non-perturbative test bed for loop quantum gravity techniques despite being perturbatively non-renormalizable.

Contribution

It presents a solvable geometric model with a true Hamiltonian and local symmetries, useful for exploring non-perturbative quantum gravity methods.

Findings

The model has a well-defined Hamiltonian and local constraints.

It offers a non-perturbative framework for loop quantum gravity.

Perturbative non-renormalizability does not hinder its utility.

Abstract

We study a type of geometric theory with a non-dynamical one-form field. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian, together with spatial diffeomorphism and Gauss law constraints, which generate the only local symmetries. Although perturbatively non-renormalizable, the model provides a test bed for the non-perturbative quantization techniques of loop quantum gravity.