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

Understand

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.