Towards a dual formulation of quantum gravity via metric-curvature bijections

TL;DR

This paper establishes a dual formulation of quantum gravity by demonstrating a one-to-one correspondence between Riemannian metrics and curvature 2-forms, offering a new change of variables for quantum gravity models.

Contribution

It introduces a novel dual formulation of quantum gravity based on metric-curvature bijections in normal coordinates, facilitating alternative approaches in the field.

Findings

Proves a one-to-one correspondence between metrics and curvature forms.

Suggests a new variable change in the operator formalism for quantum gravity.

Potential applications in asymptotic safety approaches.

Abstract

We prove that Riemannian metrics in General Relativity in the \emph{`normal-coordinates'} gauge are in one-to-one correspondence with curvature 2-forms. We discuss how this can be used as a change of variables in the operator formalism to construct a dual formulation of quantum gravity pertinent in the context of asymptotic safety-like approaches to quantum gravity.