Dynamical torsion in view of a distinguished class of Dirac operators

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.