On the topological reduction from the affine to the orthogonal gauge theory of gravity

TL;DR

This paper demonstrates how metric-affine gauge theories of gravity can be simplified to Riemann-Cartan theories using fibre bundle theory, introducing matter fields and proposing a quantum gravity framework.

Contribution

It provides a topological reduction method from affine to orthogonal gauge theories of gravity and suggests a new approach for quantum gravity development.

Findings

Metric-affine gauge theory reduces to Riemann-Cartan theory.

Matter fields emerge from nonmetric degrees of freedom.

A potential framework for quantum gravity is proposed.

Abstract

Making use of the fibre bundle theory to describe metric-affine gauge theories of gravity we are able to show that metric-affine gauge theory can be reduced to the Riemann-Cartan one. The price we pay for simplifying the geometry is the presence of matter fields associated with the nonmetric degrees of freedom of the original setup. Also, a possible framework for the construction of a quantum gravity theory is developed along the text.