Einstein-Cartan-Dirac Theory in (1+2)-Dimensions

TL;DR

This paper formulates Einstein-Cartan-Dirac theory in (1+2) dimensions using differential forms, deriving field equations, and finding exact solutions that reduce to AdS_3 geometry without a Dirac field.

Contribution

It introduces a novel formulation of Einstein-Cartan-Dirac theory in lower dimensions and derives exact solutions with specific symmetry properties.

Findings

Torsion is algebraically related to the Dirac field.

Exact circularly symmetric solutions are obtained.

Solutions reduce to AdS_3 geometry when the Dirac field is absent.

Abstract

Einstein-Cartan theory is formulated in (1+2)-dimensions using the algebra of exterior differential forms. A Dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. The space-time torsion is found to be given algebraically in terms of the Dirac field. Circularly symmetric, exact solutions that collapse to AdS_3 geometry in the absence of a Dirac spinor are found.