Dynamical torsion in view of a distinguished class of Dirac operators

TL;DR

This paper explores geometric torsion through a special class of Dirac operators, deriving a variational principle akin to Yang-Mills theory, leading to propagating torsion in vacuum unlike traditional Einstein-Cartan theory.

Contribution

It introduces a novel approach linking Dirac operators to torsion, resulting in a variational framework that predicts propagating torsion in vacuum.

Findings

Derivation of a variational problem for torsion from Dirac operators

Prediction of propagating torsion in vacuum

Comparison with Einstein-Cartan theory showing new dynamics

Abstract

In this paper we discuss geometric torsion in terms of a distinguished class of Dirac operators. We demonstrate that from this class of Dirac operators a variational problem for torsion can be derived similar to that of Yang-Mills gauge theory. As a consequence, one ends up with propagating torsion even in vacuum as opposed to Einstein-Cartan theory.